Kaleem Quraishi - Academia.edu (original) (raw)

Papers by Kaleem Quraishi

In this paper, we obtain solutions of some multiple series identities involving bounded multiple ... more In this paper, we obtain solutions of some multiple series identities involving bounded multiple sequences. We also derive hypergeometric forms of these identities involving Kamp´ e de F´ eriet double hypergeometric

International Journal of Mathematical Archive, 2013

I n the present paper we evaluate two definite integrals of Boros and Moll with certain convergen... more I n the present paper we evaluate two definite integrals of Boros and Moll with certain convergence conditions, by means of Leibnitz rule for differentiation under integral sign and Wallis' formula in systematic way.

In the present work, we provide the exact equation of motion of a simple pendulum of arbitrary am... more In the present work, we provide the exact equation of motion of a simple pendulum of arbitrary amplitude. For flrst time, a new and exact expression is obtained for the time \t" of swinging of a simple pendulum from the vertical position to an arbitrary angular position \µ". The time period \T" of such a pendulum is also exactly expressible in terms of hypergeometric functions.

Global Journal of Science Frontier Research, 2011

Present paper concernsmainly with verififification and extension of the table for (1),, (2),, (3)... more Present paper concernsmainly with verififification and extension of the table for (1),, (2),, (3),,.........,,, (30) of Ramanujan. Our extended table for (31),, (32),, (33),,.........,,, (211) is obtained without using certain arithmetical functionsdefififined by Ramanujan and also the theory of elliptic functions.

In this paper, we construct two quadratic transformations influenced by the work of Kummer and ap... more In this paper, we construct two quadratic transformations influenced by the work of Kummer and application of hypergeometric summation theorems of argument “two”. Further, we establish some generalizations of these quadratic transformations in terms of double series identities having the bounded sequence. Three reduction formulas for Kampé de Fériet’s double hypergeometric functions are also obtained as special cases.

International Journal of Mathematics Trends and Technology, 2019

Journal of Computer and Mathematical Sciences, 2019

Journal of Computer and Mathematical Sciences, 2018

Motivated by the evaluation of indefinite integrals of sin(ax 2 +bx+c), cos(ax 2 -bx+c) and exp(a... more Motivated by the evaluation of indefinite integrals of sin(ax 2 +bx+c), cos(ax 2 -bx+c) and exp(ax 2 +bx+c) in terms of Fresnel’s integrals, error function, complementary error function and probability integral; we obtain some indefinite integrals of the product of polynomial function and generalized hypergeometric function A F B (whose argument is another polynomial function) in terms of multivariable hypergeometric function of Srivastava-Daoust. Making suitable adjustments of parameters and variables in our indefinite integrals and using hypergeometric forms of special functions and elementary functions, we can find a number of known and unknown indefinite integrals of transcendental functions and special functions.

Acta Mathematica Scientia

Using series iteration techniques, we derive a number of general double series identities and app... more Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduc- tion formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon

We obtain four new transformations relating double hypergeometric functions of Elxton and Kampé d... more We obtain four new transformations relating double hypergeometric functions of Elxton and Kampé de Fériet, using series rearrangement techniques and well known transformations of Euler and Whipple.

In 1984, Exton generalized and unified some double hypergeometric functions of Horn. In this pape... more In 1984, Exton generalized and unified some double hypergeometric functions of Horn. In this paper, we obtain two infinite sums for Exton’s double hypergeometric G-function by series rearrangement technique.

Motivated by the works of L.J. Slater and A. Verma, we have derived some results on truncated uni... more Motivated by the works of L.J. Slater and A. Verma, we have derived some results on truncated unilateral generalized hypergeometric series of positive unit argument subject to certain conditions in numerator and denominator param- eters. The results presented here are presumably new.

In this paper we obtain some summation theorems for truncated bilateral generalized hypergeometri... more In this paper we obtain some summation theorems for truncated bilateral generalized hypergeometric series involving h g H 2 2 ] 1 ;) (), (1 ;) (1), [(using series iteration techniques; where η υ ϕ ρ ϖ ε , , , , , and E Ξ are the functions of parameters . h h h g g g Applying Rainville's limit formula for certain infinite products, some non terminating bilateral hypergeometric summation theorems with negative unit argument are also deduced, in terms of Gamma functions subject to certain conditions. The results presented here are presumably new.

In this paper, we obtain successive differentiation and change of argument associated with Gould-... more In this paper, we obtain successive differentiation and change of argument associated with Gould-Hopper polynomials. We also derived generalized Curzon's integral and linear generating relations.

We obtain numerical values of sixty one hypergeometric summation theorems of argument (-1) in the... more We obtain numerical values of sixty one hypergeometric summation theorems of argument (-1) in the form of 2n+1 F 2n 1,1,⋯,1 ︷ (2n+1)times ;2,2,⋯,2 ︸ 2ntimes ;-1and 2n+2 F 2n+1 1 2,1 2,⋯,1 2 ︷ (2n+1)times ,1;3 2,3 2,⋯,3 2 ︸ (2n+1)times ;-1 by means of Bernoulli’s and Euler’s numbers.

We obtain numerical values of sixty hypergeometric summation theorems of unit argument in the for... more We obtain numerical values of sixty hypergeometric summation theorems of unit argument in the form of 2n+1 F 2n 1,1,⋯,1 ︷ (2n+1)times ;2,2,, ˙2 ︸ 2ntimes ;1and 2n+1 F 2n 1 2,1 2,⋯,1 2 ︷ 2ntimes ,1;3 2,3 2,⋯3 2 ︸ 2ntimes ;1 for n=1,2,3,⋯,30, by of Bernoulli’s numbers.

We obtain some new hypergeometric transformations associated with double hypergeometric functions... more We obtain some new hypergeometric transformations associated with double hypergeometric functions of Kampé de Fériet and Exton, using integral operational techniques. Some known results of Saran and Karlsson are obtained as special cases.

We have established two new theorems associated with truncated and terminating hypergeometric ser... more We have established two new theorems associated with truncated and terminating hypergeometric series, using series iteration technique.