Vol. 30, No. 2, 1969

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ISSN: 0030-8730
A note on certain dual series equations involving Laguerre polynomials

H. M. (Hari Mohan) Srivastava

Vol. 30 (1969), No. 2, 525–527
Abstract

In this paper an exact solution is obtained for the dual series equations

n=0----An-----
Γ (α+ n + 1)Ln(α)(x) = f(x), 0 x < y, (1)
n=0    A
-----n-----
Γ (α+ β + n)Ln(σ)(x) = g(x), y < x < , (2)
where α + β + 1 > β > 1 m,σ + 1 > α + β > 0,m is a positive integer,
         (     )
L (αn)(x) = α + n  1F1[− n;α + 1;x],
n

is the Laguerre polynomial and f(x) and g(x) are prescribed functions.

Mathematical Subject Classification
Primary: 45.20
Secondary: 33.00
Milestones
Received: 20 January 1969
Published: 1 August 1969
Authors
H. M. (Hari Mohan) Srivastava