International Journal of Mathematics Trends and Technology
Volume 39 | Number 3 | Year 2016 | Article Id. IJMTT-V39P525 | DOI : https://doi.org/10.14445/22315373/IJMTT-V39P525
The object of the paper is to establish an integral formula involving the generalized prolate spheroidal wave function, generalized hypergeometric function, generalized polynomials, Aleph-function of one variable and multivariable I-function. This integral formula has been employed to obtain an expansion formula for multivariable I-function, generalized hypergeometric function, a class of polynomial and Aleph-function in terms of generalized prolate spheroidal wave function.This expansion formula being of very general nature can be transformed to provide many new results involving various commonly used special functions occuring in applied mathematics, mathematics physics and mchanics. During the course of finding, we establish several particular cases.
[1] Chaurasia V.B.L and Singh Y. New generalization of integral equations of fredholm type using Aleph-function Int. J. of Modern Math. Sci. 9(3), 2014, p 208-220.
[2] Erdelyi A. et al Tables of integral transforms,Vol II. Mc. Graw-Hill, New York (1954).
[3] Gupta R.K. Generalized prolate spheroidal wave functions. Proc. India. Acad. Sci 85A (2), (1977),page 104-114.
[4] Y.N. Prasad , Multivariable I-function , Vijnana Parishad Anusandhan Patrika 29 ( 1986 ) , page 231-237.
[5] Sharma S.D. Multiple generalized prolate spheroidal wave transforms and its applications . Kyungpook Mathematical Journal, Vol 20 (1) ,( 1980), page 121-127.
[6] Srivastava H.M. A multilinear generating function for the Konhauser set of biorthogonal polynomials suggested by Laguerre polynomial, Pacific. J. Math. 177(1985), page183-191.
[7] H.M. Srivastava And R.Panda. Some expansion theorems and generating relations for the H-function of several complex variables. Comment. Math. Univ. St. Paul. 24(1975), p.119-137.
[8] Südland N.; Baumann, B. and Nonnenmacher T.F. , Open problem : who knows about the Aleph-functions? Fract. Calc. Appl. Anal., 1(4) (1998): 401-402.
Frédéric Ayant, "Fourier expansion of generalized prolate spheroidal wave function concerning generalized polynomials ,Aleph-function and multivariable I-function," International Journal of Mathematics Trends and Technology (IJMTT), vol. 39, no. 3, pp. 206-214, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V39P525
PDF 
Abstract 
Keywords 
References 
Citation