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

Understand

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.