Bilinear and bilateral generating functions of generalized polynomials

Mohammad, Ch. Wali

doi:10.1017/s0334270000008833

Cited by 7 publications

(4 citation statements)

References 15 publications

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“…Use Eq (29) take the first partial derivative with respect to k and set k = −1 and simplify using Eq (13) and the Pochhammer symbol equation given by…”

Section: Resultsmentioning

confidence: 99%

“…In the work by Mason [11] the bivariate form of Chebyshev polynomials was employed in studying polynomial approximation. Examples of bilateral generating functions and their derivations are detailed in chapter 1 in McBride [12] and in the work by Mohammad [13]. The Chebyshev polynomial has also been studied and used in numerical solutions of initial boundary equations [14][15][16].…”

Section: Recent Developmentsmentioning

confidence: 99%

“…Solutions of partial differential equations in terms of two-dimensional Cbebyshev series have been studied with possible applications to the eigenvalue problem for a vibrating L-shaped membrane. In this work we provide a closed form solution to the bilateral generating function featuring the double summation of Chebyshev polynomials expressed in terms of the incomplete gamma function similar to the forms given in the works [12,13]. In section 3, the Chebyshev contour integral formula is derived.…”

Section: Recent Developmentsmentioning

confidence: 99%

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Chebyshev series: Derivation and evaluation

Reynolds

Stauffer

2023

PLoS ONE

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In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial are also derived and summarized. Special cases are evaluated in terms of composite forms of both Chebyshev polynomials and the incomplete gamma function.

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“…Use Eq (29) take the first partial derivative with respect to k and set k = −1 and simplify using Eq (13) and the Pochhammer symbol equation given by…”

Section: Resultsmentioning

confidence: 99%

Section: Recent Developmentsmentioning

confidence: 99%

Section: Recent Developmentsmentioning

confidence: 99%

See 1 more Smart Citation

Chebyshev series: Derivation and evaluation

Reynolds

Stauffer

2023

PLoS ONE

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“…Such generalized and new families of elliptic-type integrals play an important role in evaluation of a number of Euler-type integrals involving various generating functions. The basic idea of evolving the theorems discussed in this article is inspired by the research work of Mohammed [23], Saran [28] and Srivastava and Yeh [39].…”

Section: Introductionmentioning

confidence: 99%

On certain generalized families of unified elliptic-type integrals pertaining to Euler integrals and generating functions

Chaurasia

Pandey

2009

Rend. Circ. Mat. Palermo

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Elliptic-type integrals have their importance and potential in certain problems in radiation physics and nuclear technology. A number of earlier works on the subject contains several interesting unifications and generalizations of some significant families of elliptic-type integrals. The present paper is intended to obtain certain new theorems on generating functions. The results obtained in this paper are of manifold generality and basic in nature. Beside deriving various known and new elliptic-type integrals and their generalizations these theorems can be used to evaluate various Euler-type integrals involving a number of generating functions.

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