A Quadratic Transformation Identity for the Confluent Heun Function Involving Three Arbitrary Parameters
摘要
We present a new quadratic transformation identity for the confluent Heun function. The transformation represents the confluent Heun function, with three arbitrary parameters of its differential equation, as the product of an exponential pre-factor and an irreducible linear combination of two confluent Heun functions with a quadratic argument and altered parameters. This result is an independent addition to the class of quadratic transformations for the confluent Heun function, distinct from the first identity of this kind reported in Heliyon 10, e36535 (2024). The new relation provides additional insights into the structure of the confluent Heun function and may prove valuable for addressing intricate mathematical models in quantum mechanics, general relativity, and related fields.