Tabinda Nahid - Academia.edu (original) (raw)

Papers by Tabinda Nahid

Research paper thumbnail of Orthogonality Associated with Bessel-Type Sheffer Sequences with Q-Parameters

Mathematical Notes, Apr 1, 2022

Research paper thumbnail of Matrix Approaches for Gould–Hopper–Laguerre–Sheffer Matrix Polynomial Identities

Axioms

The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational met... more The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them using matrix techniques. By leveraging properties of Pascal functionals and Wronskian matrices, we derive several identities for these polynomials, including recurrence relations. It is highlighted that these identities, acquired via matrix techniques, are distinct from the ones obtained when using operational methods.

Research paper thumbnail of Differential equations for certain hybrid special matrix polynomials

Boletim da Sociedade Paranaense de Matemática, Dec 24, 2022

Research paper thumbnail of An Algebraic Approach to Degenerate Appell Polynomials and Their Hybrid Forms via Determinants

Acta Mathematica Scientia

Research paper thumbnail of Rotating radial vibrations in human bones (femoral, mandibular and tibia) and crystals (Mg, Co, Cd, Zn and beryl) made cylindrical shell under magnetic field and hydrostatic stress

Mechanics of Advanced Materials and Structures

Research paper thumbnail of 2-Variable Fubini-degenerate Apostol-type polynomials

Asian-European Journal of Mathematics

This work deals with the mathematical inspection of a hybrid family of the degenerate polynomials... more This work deals with the mathematical inspection of a hybrid family of the degenerate polynomials of the Apostol-type. The inclusion of the derivation of few series expansion formulas, explicit representations and difference equations for this hybrid family brings a novelty to the existing literature. Moreover, certain connection formulas and several novel identities for these polynomials are established and investigated. The graphical representations of certain degenerate polynomials are explored and several new interesting pattern of the zeros are observed.

Research paper thumbnail of Finding non-linear differential equations and certain identities for the Bernoulli–Euler and Bernoulli–Genocchi numbers

SN Applied Sciences, 2019

In this research paper, the authors derived the non-linear differential equations for certain hyb... more In this research paper, the authors derived the non-linear differential equations for certain hybrid special polynomials related to the Bernoulli polynomials. The families of non-linear differential equations arising from the generating functions of the Bernoulli-Euler and Bernoulli-Genocchi polynomials are derived. Further, these non-linear differential equations are used to derive certain identities and formulas for the Bernoulli-Euler and Bernoulli-Genocchi numbers. However, to provided an exception, a linear differential equation is derived from the generating function of the Genocchi-Euler polynomials.

Research paper thumbnail of Connection problems and matrix representations for certain hybrid polynomials

Tbilisi Mathematical Journal, 2018

Research paper thumbnail of Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials

Mathematics, 2018

The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite... more The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed.

Research paper thumbnail of Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials

Mathematics, 2018

The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite... more The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed.

Research paper thumbnail of On degenerate Apostol-type polynomials and applications

Boletín de la Sociedad Matemática Mexicana, 2018

The main object of the current paper is to introduce and investigate a new unified class of the d... more The main object of the current paper is to introduce and investigate a new unified class of the degenerate Apostol-type polynomials. These polynomials are studied by means of the generating function, series definition and are framed within the context of monomiality principle. Several important recurrence relations and explicit representations for the antecedent class of polynomials are derived. As the special cases, the degenerate Apostol-Bernoulli, Euler and Genocchi polynomials are obtained and corresponding results are also proved. A fascinating example is constructed in terms of truncated-exponential polynomials, which gives the applications of these polynomials to produce their hybridized forms.

Research paper thumbnail of Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family

Fractal and Fractional

The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hop... more The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques. The generating function and operational representations for this new family of polynomials will be established. In addition, these specific matrix polynomials are interpreted in terms of quasi-monomiality. The extended versions of the Gould-Hopper-Laguerre-Sheffer matrix polynomials are introduced, and their characteristics are explored using the integral transform. Further, examples of how these results apply to specific members of the matrix polynomial family are shown.

Research paper thumbnail of Certain properties of the Laguerre-Sheffer polynomials

Research paper thumbnail of Finding determinant and integral forms of the 2-iterated 2D Appell polynomials

The Journal of Analysis

This article deals with the derivation of determinant and integral forms for the 2-iterated 2 D A... more This article deals with the derivation of determinant and integral forms for the 2-iterated 2 D Appell polynomials. The summation formulae and operational rule for these polynomials are derived. Also, certain identities for these polynomials are established by using operational formalism. The exponential operational definitions and integral representations are combined to introduce the extended form of these 2-iterated 2 D Appell polynomials. Further, by using computer-aided programs (Mathematica or Matlab), we draw graphs of some particular cases of the 2-iterated 2 D Appell polynomials, mainly in order to observe in several angles how zeros of these polynomials are distributed and located.

Research paper thumbnail of Properties of Certain Hybrid Forms of Special Polynomials and q Special Polynomials

Research paper thumbnail of Certain results for unified Apostol type-truncated exponential-Gould-Hopper polynomials and their relatives

arXiv: General Mathematics, 2020

The present article aims to introduce a unified family of the Apostol type-truncated exponential-... more The present article aims to introduce a unified family of the Apostol type-truncated exponential-Gould-Hopper polynomials and to characterize its properties via generating functions. A unified presentation of the generating function for the Apostol type-truncated exponential-Gould-Hopper polynomials is established and its applications are given. By the use of operational techniques, the quasi-monomial properties for the unified family are proved. Several explicit representations and multiplication formulas related to these polynomials are obtained. Some general symmetric identities involving multiple power sums and Hurwitz-Lerch zeta functions are established by applying different analytical means on generating functions.

Research paper thumbnail of Certain Results Associated with Hybrid Relatives of the q-Sheffer Sequences

abstract: The intended objective of this paper is to introduce a new class of the hybrid q-Sheffe... more abstract: The intended objective of this paper is to introduce a new class of the hybrid q-Sheffer polynomials by means of the generating function and series definition. The determinant definition and other striking properties of these polynomials are established. Certain results for the continuous q-Hermite-Appell polynomials are obtained. The graphical depictions are performed for certain members of the hybrid q-Sheffer family. The zeros of these members are also explored using numerical simulations. Finally, the orthogonality condition for the hybrid q-Sheffer polynomials is established.

Research paper thumbnail of Certain properties of the Laguerre–Sheffer polynomials

The Journal of Analysis, 2021

Research paper thumbnail of q-difference equations for the composite 2D q-Appell polynomials and their applications

soon as possible after acceptance. Copyediting, typesetting, and review of the resulting proof wi... more soon as possible after acceptance. Copyediting, typesetting, and review of the resulting proof will be undertaken on this manuscript before final publication of the Version of Record (VoR). Please note that during production and pre-press, errors may be discovered which could affect the content.

Research paper thumbnail of Several characterizations of Bessel functions and their applications

Georgian Mathematical Journal

The present work deals with the mathematical investigation of some generalizations of Bessel func... more The present work deals with the mathematical investigation of some generalizations of Bessel functions. The main motive of this paper is to show that the generating function can be employed efficiently to obtain certain results for special functions. The complex form of Bessel functions is introduced by means of the generating function. Certain enthralling properties for complex Bessel functions are investigated using the generating function method. By considering separately the real and the imaginary part of complex Bessel functions, we get respectively cosine-Bessel functions and sine-Bessel functions for which several novel identities and Jacobi–Anger expansions are established. Also, the generating function of degenerate Bessel functions is investigated and certain novel identities are obtained for them. A hybrid form of degenerate Bessel functions, namely, of degenerate Fubini–Bessel functions, is constructed using the replacement technique. Finally, the explicit forms of the r...

Research paper thumbnail of Orthogonality Associated with Bessel-Type Sheffer Sequences with Q-Parameters

Mathematical Notes, Apr 1, 2022

Research paper thumbnail of Matrix Approaches for Gould–Hopper–Laguerre–Sheffer Matrix Polynomial Identities

Axioms

The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational met... more The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them using matrix techniques. By leveraging properties of Pascal functionals and Wronskian matrices, we derive several identities for these polynomials, including recurrence relations. It is highlighted that these identities, acquired via matrix techniques, are distinct from the ones obtained when using operational methods.

Research paper thumbnail of Differential equations for certain hybrid special matrix polynomials

Boletim da Sociedade Paranaense de Matemática, Dec 24, 2022

Research paper thumbnail of An Algebraic Approach to Degenerate Appell Polynomials and Their Hybrid Forms via Determinants

Acta Mathematica Scientia

Research paper thumbnail of Rotating radial vibrations in human bones (femoral, mandibular and tibia) and crystals (Mg, Co, Cd, Zn and beryl) made cylindrical shell under magnetic field and hydrostatic stress

Mechanics of Advanced Materials and Structures

Research paper thumbnail of 2-Variable Fubini-degenerate Apostol-type polynomials

Asian-European Journal of Mathematics

This work deals with the mathematical inspection of a hybrid family of the degenerate polynomials... more This work deals with the mathematical inspection of a hybrid family of the degenerate polynomials of the Apostol-type. The inclusion of the derivation of few series expansion formulas, explicit representations and difference equations for this hybrid family brings a novelty to the existing literature. Moreover, certain connection formulas and several novel identities for these polynomials are established and investigated. The graphical representations of certain degenerate polynomials are explored and several new interesting pattern of the zeros are observed.

Research paper thumbnail of Finding non-linear differential equations and certain identities for the Bernoulli–Euler and Bernoulli–Genocchi numbers

SN Applied Sciences, 2019

In this research paper, the authors derived the non-linear differential equations for certain hyb... more In this research paper, the authors derived the non-linear differential equations for certain hybrid special polynomials related to the Bernoulli polynomials. The families of non-linear differential equations arising from the generating functions of the Bernoulli-Euler and Bernoulli-Genocchi polynomials are derived. Further, these non-linear differential equations are used to derive certain identities and formulas for the Bernoulli-Euler and Bernoulli-Genocchi numbers. However, to provided an exception, a linear differential equation is derived from the generating function of the Genocchi-Euler polynomials.

Research paper thumbnail of Connection problems and matrix representations for certain hybrid polynomials

Tbilisi Mathematical Journal, 2018

Research paper thumbnail of Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials

Mathematics, 2018

The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite... more The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed.

Research paper thumbnail of Determinant Forms, Difference Equations and Zeros of the q-Hermite-Appell Polynomials

Mathematics, 2018

The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite... more The present paper intends to introduce the hybrid form of q-special polynomials, namely q-Hermite-Appell polynomials by means of generating function and series definition. Some significant properties of q-Hermite-Appell polynomials such as determinant definitions, q-recurrence relations and q-difference equations are established. Examples providing the corresponding results for certain members belonging to this q-Hermite-Appell family are considered. In addition, graphs of certain q-special polynomials are demonstrated using computer experiment. Thereafter, distribution of zeros of these q-special polynomials is displayed.

Research paper thumbnail of On degenerate Apostol-type polynomials and applications

Boletín de la Sociedad Matemática Mexicana, 2018

The main object of the current paper is to introduce and investigate a new unified class of the d... more The main object of the current paper is to introduce and investigate a new unified class of the degenerate Apostol-type polynomials. These polynomials are studied by means of the generating function, series definition and are framed within the context of monomiality principle. Several important recurrence relations and explicit representations for the antecedent class of polynomials are derived. As the special cases, the degenerate Apostol-Bernoulli, Euler and Genocchi polynomials are obtained and corresponding results are also proved. A fascinating example is constructed in terms of truncated-exponential polynomials, which gives the applications of these polynomials to produce their hybridized forms.

Research paper thumbnail of Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family

Fractal and Fractional

The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hop... more The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques. The generating function and operational representations for this new family of polynomials will be established. In addition, these specific matrix polynomials are interpreted in terms of quasi-monomiality. The extended versions of the Gould-Hopper-Laguerre-Sheffer matrix polynomials are introduced, and their characteristics are explored using the integral transform. Further, examples of how these results apply to specific members of the matrix polynomial family are shown.

Research paper thumbnail of Certain properties of the Laguerre-Sheffer polynomials

Research paper thumbnail of Finding determinant and integral forms of the 2-iterated 2D Appell polynomials

The Journal of Analysis

This article deals with the derivation of determinant and integral forms for the 2-iterated 2 D A... more This article deals with the derivation of determinant and integral forms for the 2-iterated 2 D Appell polynomials. The summation formulae and operational rule for these polynomials are derived. Also, certain identities for these polynomials are established by using operational formalism. The exponential operational definitions and integral representations are combined to introduce the extended form of these 2-iterated 2 D Appell polynomials. Further, by using computer-aided programs (Mathematica or Matlab), we draw graphs of some particular cases of the 2-iterated 2 D Appell polynomials, mainly in order to observe in several angles how zeros of these polynomials are distributed and located.

Research paper thumbnail of Properties of Certain Hybrid Forms of Special Polynomials and q Special Polynomials

Research paper thumbnail of Certain results for unified Apostol type-truncated exponential-Gould-Hopper polynomials and their relatives

arXiv: General Mathematics, 2020

The present article aims to introduce a unified family of the Apostol type-truncated exponential-... more The present article aims to introduce a unified family of the Apostol type-truncated exponential-Gould-Hopper polynomials and to characterize its properties via generating functions. A unified presentation of the generating function for the Apostol type-truncated exponential-Gould-Hopper polynomials is established and its applications are given. By the use of operational techniques, the quasi-monomial properties for the unified family are proved. Several explicit representations and multiplication formulas related to these polynomials are obtained. Some general symmetric identities involving multiple power sums and Hurwitz-Lerch zeta functions are established by applying different analytical means on generating functions.

Research paper thumbnail of Certain Results Associated with Hybrid Relatives of the q-Sheffer Sequences

abstract: The intended objective of this paper is to introduce a new class of the hybrid q-Sheffe... more abstract: The intended objective of this paper is to introduce a new class of the hybrid q-Sheffer polynomials by means of the generating function and series definition. The determinant definition and other striking properties of these polynomials are established. Certain results for the continuous q-Hermite-Appell polynomials are obtained. The graphical depictions are performed for certain members of the hybrid q-Sheffer family. The zeros of these members are also explored using numerical simulations. Finally, the orthogonality condition for the hybrid q-Sheffer polynomials is established.

Research paper thumbnail of Certain properties of the Laguerre–Sheffer polynomials

The Journal of Analysis, 2021

Research paper thumbnail of q-difference equations for the composite 2D q-Appell polynomials and their applications

soon as possible after acceptance. Copyediting, typesetting, and review of the resulting proof wi... more soon as possible after acceptance. Copyediting, typesetting, and review of the resulting proof will be undertaken on this manuscript before final publication of the Version of Record (VoR). Please note that during production and pre-press, errors may be discovered which could affect the content.

Research paper thumbnail of Several characterizations of Bessel functions and their applications

Georgian Mathematical Journal

The present work deals with the mathematical investigation of some generalizations of Bessel func... more The present work deals with the mathematical investigation of some generalizations of Bessel functions. The main motive of this paper is to show that the generating function can be employed efficiently to obtain certain results for special functions. The complex form of Bessel functions is introduced by means of the generating function. Certain enthralling properties for complex Bessel functions are investigated using the generating function method. By considering separately the real and the imaginary part of complex Bessel functions, we get respectively cosine-Bessel functions and sine-Bessel functions for which several novel identities and Jacobi–Anger expansions are established. Also, the generating function of degenerate Bessel functions is investigated and certain novel identities are obtained for them. A hybrid form of degenerate Bessel functions, namely, of degenerate Fubini–Bessel functions, is constructed using the replacement technique. Finally, the explicit forms of the r...