On dual series relations involving Laguerre polynomials

K. N. Srivastava

Vol. 19 (1966), No. 3, 529–533

DOI: 10.2140/pjm.1966.19.529

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 + 1∕2)}L nα(x)	= f 2(x), y < x ≦∞,α > −1∕2,

where L_n^α(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)