Vol. 19, No. 3, 1966

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On dual series relations involving Laguerre polynomials

K. N. Srivastava

Vol. 19 (1966), No. 3, 529–533
Abstract

In this paper, we shall consider the problem determining the sequence {An}, such that

n=0{An∕Γ(n + α + 1)}L nα(x) = f 1(x), 0 x < y,
n=0{An∕Γ(n + α + 12)}L nα(x) = f 2(x), y < x ,α > 12,
where Lnα(x) is a Laguerre polynomial, the functions f1(x) and f2(x) being prescribed. By expressing the sequence {An} in terms of a sequence of integrals involving an unknown function g(u) the problem is reduced to that of solving an Abel integral equation for g(u).

Mathematical Subject Classification
Primary: 42.16
Milestones
Received: 29 June 1965
Published: 1 December 1966
Authors
K. N. Srivastava