1962/12/01 by Roop Narain 路 1 citation
Mathematics 路 Physics and Astronomy 路 #Mathematical functions and polynomials #Differential Equations and Boundary Problems #Quantum Mechanics and Non-Hermitian Physics #Bessel function #Mathematics #Struve function #Function (biology) #Hypergeometric function #Fourier transform #Simple (philosophy) #Generalized hypergeometric function #Combinatorics #Fourier series #Pure mathematics #Kernel (algebra) #Mathematical analysis #Orthogonal polynomials
paper 路 pdf 路 doi:10.1090/s0002-9939-1962-0144157-5
openalex publication_date 1962/12/01 路 openalex created_date 2016/06/24 路 openalex updated_date 2026/04/06
A simple example of the formula (1.3) is that in which K(x) = xll2'Y(x) and H(x) = x111H,(x), where Y,(x) denotes the Bessel function of the first kind and H,(x) the Struve's function [4, p. 64 and p. 328]. The functions K(x) and H(x) have been referred to as a pair of unsymmetrical Fourier kernels by various authors. The object of this paper is to obtain a new pair of kernels K(x), H(x) in terms of the most general G-function satisfying (1.3). The G-function is a sum of hypergeometric functions each of which is usually an entire function. It is written as on the left of (1.4) below and defined [2, p. 207] by the integral on the right