On the Trigonometric Developments of Certain Doubly Periodic Functions of the Second Kind

Authors

M. A. Basoco, University of Nebraska - Lincoln

Document Type

Article

Date of this Version

8-1932

Comments

Published in Bull. Amer. Math. Soc. 38 (1932) 560-568. Used by permission.

Abstract

The class of meromorphic functions which satisfy periodicity relations of the form (1) ƒ(z + 2ω_l) = c₁f(z), f(z + 2ω₂) = c₂f{z), where the multipliers c₁ and c₂ are independent of z, and ω_l/ω₂ is a complex number with non-vanishing imaginary part, has been named by Hermite doubly periodic of the second kind. It is possible to make the study of these functions depend on others of the same type, but such that one of the multipliers, say c_l, is unity. In what follows we shall assume, further, that the periods (2ω_l, 2ω₂) are (π, πτ), where τ = a +ib, b>0.