Prakriti Rai - Academia.edu (original) (raw)

Papers by Prakriti Rai

Boletim da Sociedade Paranaense de Matemática, May 23, 2024

South East Asian J. of Mathematics and Mathematical Sciences

In this article, by means of the extended beta function, we introduce new extension of the genera... more In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem). We also consider some new and known results as consequences of our proposed extension of the generalized τ -Gauss hypergeometric function.

The Journal of the Indian Mathematical Society

In this paper, we have introduced the multi-indexed Whittaker function (3m-parameter) by using th... more In this paper, we have introduced the multi-indexed Whittaker function (3m-parameter) by using the extended confluent hypergeometric function which is defined in terms of multi-indexed (3m-parameter) Mittag-Leffler function. We derive some properties of multi-indexed (3m-parameter) Whittaker function such as its integral representations, derivative formula and Hankel transform.

South East Asian J. of Mathematics and Mathematical Sciences

In this article, by means of the extended beta function, we introduce new extension of the genera... more In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem). We also consider some new and known results as consequences of our proposed extension of the generalized τ -Gauss hypergeometric function.

Recently, an extension of τ Gauss hypergeometric function was obtained in terms of the extended v... more Recently, an extension of τ Gauss hypergeometric function was obtained in terms of the extended version of the pochhammer symbol[11]. We have established some properties on further generalization of the extended τ Gauss hypergeometric function containing extra parameters. We have also established some other properties and relationships involving the integral representations, derivative formulas and Mellin transforms.

South East Asian J. of Mathematics and Mathematical Sciences

In this paper, we introduce a generalized form of Whittaker function with the help of generalized... more In this paper, we introduce a generalized form of Whittaker function with the help of generalized confluent k-hypergeometric function. We establish several interesting properties of the Whittaker k-function such as its integral representations, derivative, Laplace transform and Hankel transform. Further, we investigate the Riemann-Liouville fractional integral and k-Riemann-Liouville fractional integral of Whittaker k-function. Some intriguing particular cases of the main results are also mentioned.

The Journal of the Indian Mathematical Society

A generalization of Humbert-Hermite polynomials is de?ned in this paper. Moreover, several genera... more A generalization of Humbert-Hermite polynomials is de?ned in this paper. Moreover, several generalizations of Hermite-Gegenbauer polynomials, Hermite-Legendre and Hermite-Chebyshev polynomials are established.

The aim of this paper is to study certain properties of generalized Apostol-Hermite-Euler polynom... more The aim of this paper is to study certain properties of generalized Apostol-Hermite-Euler polynomials with three parameters. We have shown that there is an intimate connection between these polynomials and established their elementary properties. We also established some identities by applying the generating functions and deduce their special cases and applications

In recent years, various mathematicians (such as Ernst, U. Duran) introduced an extension of Apos... more In recent years, various mathematicians (such as Ernst, U. Duran) introduced an extension of Apostol Type polynomials of order α. Recently, W. A. Khan introduced a new class of qHermite based Apostol type polynomials. Motivated by their research, this article introduces a new class of (p,q)analogue of Hermite based Apostol type polynomials of order α and investigate its characteristics.In particular, it establishes the generating function, series expression and explicit relation for these polynomials. It also explores the relationship between generalized Bernoulli, Euler and Genocchi polynomials.

Journal of the Indian Mathematical Society, 2018

There emerges different extended versions of Beta function and hypergeometric functions containin... more There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.

In this paper a theorem for general multiple series is established using Dixon's theorem and ... more In this paper a theorem for general multiple series is established using Dixon's theorem and Srivastava's identities. The theorem proved in this paper provides new transformations and connections with various classes of well known hyper geometric functions and even new representations for special cases of these functions.

The Journal of the Indian Mathematical Society, 2020

In this paper, we have generalized Apostol-Hermite-Bernoullli polynomials, Apostol-Hermite-Euler ... more In this paper, we have generalized Apostol-Hermite-Bernoullli polynomials, Apostol-Hermite-Euler polynomials and Apostol-Hermite-Genocchi polynomials. We have shown that there is an intimate connection between these polynomials and derived some implicit summation formulae by applying the generating functions.

International Journal of Differential Equations, 2021

Several mathematicians have extensively investigated polynomials, their extensions, and their app... more Several mathematicians have extensively investigated polynomials, their extensions, and their applications in various other research areas for a decade. Our paper aims to introduce another such polynomial, namely, Laguerre-based generalized Humbert polynomial, and investigate its properties. In particular, it derives elementary identities, recursive differential relations, additional symmetry identities, and implicit summation formulas.

Boletim da Sociedade Paranaense de Matemática, May 23, 2024

South East Asian J. of Mathematics and Mathematical Sciences

In this article, by means of the extended beta function, we introduce new extension of the genera... more In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem). We also consider some new and known results as consequences of our proposed extension of the generalized τ -Gauss hypergeometric function.

The Journal of the Indian Mathematical Society

In this paper, we have introduced the multi-indexed Whittaker function (3m-parameter) by using th... more In this paper, we have introduced the multi-indexed Whittaker function (3m-parameter) by using the extended confluent hypergeometric function which is defined in terms of multi-indexed (3m-parameter) Mittag-Leffler function. We derive some properties of multi-indexed (3m-parameter) Whittaker function such as its integral representations, derivative formula and Hankel transform.

South East Asian J. of Mathematics and Mathematical Sciences

In this article, by means of the extended beta function, we introduce new extension of the genera... more In this article, by means of the extended beta function, we introduce new extension of the generalized τ -Gauss’ hypergeometric functions and present some new integral and series representations (including the one obtained by adopt- ing the well-known Ramanujan’s Master Theorem). We also consider some new and known results as consequences of our proposed extension of the generalized τ -Gauss hypergeometric function.

Recently, an extension of τ Gauss hypergeometric function was obtained in terms of the extended v... more Recently, an extension of τ Gauss hypergeometric function was obtained in terms of the extended version of the pochhammer symbol[11]. We have established some properties on further generalization of the extended τ Gauss hypergeometric function containing extra parameters. We have also established some other properties and relationships involving the integral representations, derivative formulas and Mellin transforms.

South East Asian J. of Mathematics and Mathematical Sciences

In this paper, we introduce a generalized form of Whittaker function with the help of generalized... more In this paper, we introduce a generalized form of Whittaker function with the help of generalized confluent k-hypergeometric function. We establish several interesting properties of the Whittaker k-function such as its integral representations, derivative, Laplace transform and Hankel transform. Further, we investigate the Riemann-Liouville fractional integral and k-Riemann-Liouville fractional integral of Whittaker k-function. Some intriguing particular cases of the main results are also mentioned.

The Journal of the Indian Mathematical Society

A generalization of Humbert-Hermite polynomials is de?ned in this paper. Moreover, several genera... more A generalization of Humbert-Hermite polynomials is de?ned in this paper. Moreover, several generalizations of Hermite-Gegenbauer polynomials, Hermite-Legendre and Hermite-Chebyshev polynomials are established.

The aim of this paper is to study certain properties of generalized Apostol-Hermite-Euler polynom... more The aim of this paper is to study certain properties of generalized Apostol-Hermite-Euler polynomials with three parameters. We have shown that there is an intimate connection between these polynomials and established their elementary properties. We also established some identities by applying the generating functions and deduce their special cases and applications

In recent years, various mathematicians (such as Ernst, U. Duran) introduced an extension of Apos... more In recent years, various mathematicians (such as Ernst, U. Duran) introduced an extension of Apostol Type polynomials of order α. Recently, W. A. Khan introduced a new class of qHermite based Apostol type polynomials. Motivated by their research, this article introduces a new class of (p,q)analogue of Hermite based Apostol type polynomials of order α and investigate its characteristics.In particular, it establishes the generating function, series expression and explicit relation for these polynomials. It also explores the relationship between generalized Bernoulli, Euler and Genocchi polynomials.

Journal of the Indian Mathematical Society, 2018

There emerges different extended versions of Beta function and hypergeometric functions containin... more There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.

In this paper a theorem for general multiple series is established using Dixon's theorem and ... more In this paper a theorem for general multiple series is established using Dixon's theorem and Srivastava's identities. The theorem proved in this paper provides new transformations and connections with various classes of well known hyper geometric functions and even new representations for special cases of these functions.

The Journal of the Indian Mathematical Society, 2020

In this paper, we have generalized Apostol-Hermite-Bernoullli polynomials, Apostol-Hermite-Euler ... more In this paper, we have generalized Apostol-Hermite-Bernoullli polynomials, Apostol-Hermite-Euler polynomials and Apostol-Hermite-Genocchi polynomials. We have shown that there is an intimate connection between these polynomials and derived some implicit summation formulae by applying the generating functions.

International Journal of Differential Equations, 2021

Several mathematicians have extensively investigated polynomials, their extensions, and their app... more Several mathematicians have extensively investigated polynomials, their extensions, and their applications in various other research areas for a decade. Our paper aims to introduce another such polynomial, namely, Laguerre-based generalized Humbert polynomial, and investigate its properties. In particular, it derives elementary identities, recursive differential relations, additional symmetry identities, and implicit summation formulas.