Journal ArticleDOI
Generating functions of Pollaczek polynomials: a revisit
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TLDR
In this paper, a new proof of Wimp's formula for the associated Pollaczek polynomials Pnλz;a,b,c,d,e,f,c was presented.Abstract:
This paper is mainly devoted to generating functions of Pollaczek and other related polynomials. We first present a new proof of Wimp's formula for the associated Pollaczek polynomials Pnλz;a,b,c. ...read more
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Special Functions Of Applied Mathematics
TL;DR: The special functions of applied mathematics is universally compatible with any devices to read and is available in the book collection an online access to it is set as public so you can download it instantly.
Journal ArticleDOI
Two inequalities for the associated Pollaczek polynomials
TL;DR: In this paper, two concise inequalities for the associated Pollaczek polynomials are proved for the orthogonal expansions with positive coefficients, using Askey's theorem and triple integral representation.
Journal ArticleDOI
Certain results on generating functions related to the associated Meixner-Pollaczek polynomials
TL;DR: In this article, a new form of a generating function for the c-associated Meixner-Pollaczek polynomials was derived, which is of particular importance since its several r...
On the spherical clothoid
TL;DR: In this article , the spherical clothoid is revisited as a nonlinear spline primitive for 3-space and its Cartesian coordinate functions using confluent hypergeometric functions (the Kummer functions) and its stereographic projection onto the complex plane.
New results on the associated Meixner, Charlier, Laguerre, and Krawtchouk polynomials
TL;DR: This article gave new explicit representations for the associated Meixner, Charlier, Laguerre, and Krawtchouk polynomials and derived new generating functions and convolution-type formulas of the corresponding classical polynomial formulas.
References
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Journal ArticleDOI
Extensions of certain classical integrals of Erdélyi for Gauss hypergeometric functions
C. M. Joshi,Yashoverdhan Vyas +1 more
TL;DR: In this paper, series manipulation technique and certain classical summation theorems for hypergeometric series can be used to prove Erdelyi's integral representations for 2F1(z), originally proved using fractional calculus.
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Infinite summation formulas of double hypergeometric functions
TL;DR: In this article, the authors obtained several infinite summation formulas of double hypergeometric functions, including the infinite summations of Appell and Horn's functions, with the help of some famous summation theorems.
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Associated Jacobi-Laurent polynomials
TL;DR: The associated Jacobi-Laurent polynomials as discussed by the authors were introduced by Hendriksen and van Rossum (1986) and they have been used for approximating two-point Pade approximations to the pair of functions.
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Divided-difference equation, inversion, connection, multiplication and linearization formulae of the continuous Hahn and the Meixner–Pollaczek polynomials
TL;DR: In this article, it was shown that the continuous Hahn and the Meixner-Pollaczek polynomials are solutions of a second-order divided-difference equation of hypergeometric type.
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A note on the triple sum series for the 9j coefficient
K. Srinivasa Rao,V Rajeswari +1 more
TL;DR: In this article, it was shown that the triple sum series of Jucys and Bandzaitis for the 9j coefficient can be identified with a formal triple hypergeometric series due to Lauricella-Saran-Srivastava.