Classical analytic representations

Abstract

Mittag-Leffler-like fractional decompositions are constructed for the gamma, Jacobian elliptic and for the quotient of Bessel functions. These results illustrate a technique herein developed which permits a complete ML decomposition of a large class of meromorphic functions without resorting to any other previously derived information or knowledge of the particular function. Typically, the point of departure of this note stands in contrast to a statement in Knopp [1, p. 44], during his development of the ML decomposition of π cot ⁡ π z \pi \cot \pi z , which reads as follows: “The still undetermined entire function, G ( z ) G\left ( z \right ) , cannot be ascertained solely from the nature and position of the poles."