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On the hydrogen wave function in Momentum-space, Clifford algebra and the Generating function of Gegenbauer polynomial

, 2008
Using the quadratic transformation and the generating function method we Perform the Fourier transformation of the wave function of coordinates of hydrogen atom and we find the analytic expression of the wave function in momentum space. We derive the matrix elements between the basis to 4-dimensions and integral representation of the generating ...
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Some generating functions for Gegenbauer polynomials.

Journal für die reine und angewandte Mathematik (Crelles Journal), 1969
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Bilinear and Bilateral generating functions for the Gegenbauer Polynomials

Afyon Kocatepe University Journal of Sciences and Engineering, 2018
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Derivatives of Generalized Gegenbauer Polynomials

Theoretical and Mathematical Physics, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
García Fuertes, W., Perelomov, A. M.
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The Generalized Clifford-Gegenbauer Polynomials Revisited

Advances in Applied Clifford Algebras, 2009
By applying a method introduced by De Bie and Sommen in Clifford superanalysis, the orthogonality relations of the generalized Clifford-Gegenbauer polynomials of wavelet analysis are extended. Moreover, this new approach allows for proving new important properties of these polynomials, such as an annihilation equation, a differential equation and an ...
Hendrik De Bie, Dixan Peña Peña, Frank Sommen   +2 more
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Some bilateral generating relations involving Gegenbauer polynomials

Integral Transforms and Special Functions, 2003
In this paper, we obtain three interesting bilateral generating functions for Gegenbauer polynomials C n b (x) associated with hypergeometric polynomials 2 F 1, 1 F 2 and 3 F 2. Our results are obtained with the help of series rearrangement technique.
M. I. Qureshi, N. U. Khan, M. A. Pathan
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Generalized Gegenbauer Koornwinder’s type polynomials change of bases

AIP Conference Proceedings, 2017
In this paper we characterize the generalized Gegenbauer polynomials using Bernstein basis, and derive the matrix of transformation of the generalized Gegenbauer polynomial basis form into the Bernstein polynomial basis and vice versa.
Mohammad AlQudah, Maalee AlMheidat
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A generalization of the symmetric classical polynomials: Hermite and Gegenbauer polynomials

Integral Transforms and Special Functions, 2016
ABSTRACTIn this paper, we give new families of polynomials orthogonal with respect to a d-dimensional vector of linear functionals, d being a positive integer number, and generalizing the standard symmetric classical polynomials: Hermite and Gegenbauer.
Neila Ben Romdhane, Mohamed Gaied
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Some generating functions of modified Gegenbauer polynomials

Proceedings of the Indian Academy of Sciences - Section A, 1987
\textit{A. K. Chongdar} [J. Orissa Math. Soc. 2, No.2, 71-85 (1983; Zbl 0571.33007)] studied Gegenbauer polynomials \(C_ n^{\gamma}(x)\) to obtain generating functions by following Weisner's group-theoretic method by means of suitable interpretations to both the index and the parameter of the polynomials. Subsequently \textit{T. I. Sultan} [J.
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q-Extension of generalized Gegenbauer polynomials

Journal of Difference Equations and Applications, 2010
We study in detail a q-extension of the generalized Gegenbauer form (functional). We show that it is symmetric H q -semi-classical of class one. The moments and the integral representations are given.
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