A Certain Multiple-Parameter Expansion

Authors

• H. P. Doole, University of Nebraska - Lincoln

Document Type

Article

Date of this Version

1931

Comments

Published in Bull. Amer. Math. Soc. 37 (1931) 439-446.

Abstract

C. C. Camp has shown the convergence of the expansion of an arbitrary function in terms of the solutions of the systems of equations
X_1’ (λa₁ - Σ_i=2ⁿμ_i)X₁ = 0,
X_1’ (λa_i + μ_i)X_i = 0, (j = 2, 3, …, n),
where the a_i’s are functions of x, with the boundary conditions
X_i(-π) = X_i(π), (j = 1, 2, …, n).
In this paper it is intended to use a differential system in which the n parameters appear in each equation with a function a_jk(x_j) multiplying each. The boundary conditions will also be more general.