Vol. 38, No. 2, 1971

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Some triple integral equations

John S. Lowndes

Vol. 38 (1971), No. 2, 515–521
Abstract

In this paper we solve the triple integral equations

  −1 --Γ (ξ-+s∕δ)-
M   {Γ (ξ + β + s∕δ)Φ(s);x} = 0, 0 ≦ x < a, b < x < ∞,
(1)

  −1 --Γ (1+-η−-s∕σ)-
M   {Γ (1+ η+ α − s∕σ)Φ(s);x} = f2(x), a < x < b,
(2)

where α,β,ξ,η,δ > 0, σ > 0, are real parameters, f2(x) is a known function, Φ(s) is to be determined and

M {h(x);s} = H (s),  M −1{H(s);x} = h(x),
(3)

denote the Mellin transform of h(x) and its inversion formula respectively.

Mathematical Subject Classification 2000
Primary: 45F05
Milestones
Received: 26 May 1970
Published: 1 August 1971
Authors
John S. Lowndes