Some dual series equations involving Laguerre polynomials

John S. Lowndes

Vol. 25 (1968), No. 1, 123–127

DOI: 10.2140/pjm.1968.25.123

Abstract

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

∑ n=0∞C nΓ(α + β + n)Ln(α;x) = f(x), 0 ≦ x < d,		(1)
∑ n=0∞C nΓ(α + 1 + n)Ln(α;x) = g(x), d < x < ∞,		(2)

where α + β > 0, 0 < β < 1, L_n(α;x) = L_n^α(x) is the Laguerre polynomial and f(x) and g(x) are known functions.

Mathematical Subject Classification

Primary: 42.16

Milestones

Received: 14 April 1967

Published: 1 April 1968