Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order

Abstract

The present article reveals important properties of the confluent Heun's functions. We derive a set of novel relations for confluent Heun's functions and their derivatives of arbitrary order. Specific new subclasses of confluent Heun's functions are introduced and studied. A new alternative derivation of confluent Heun's polynomials is presented.

8 pages, no figures, LaTeX file, final version

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