New indefinite integrals of confluent Heun functions
Davide Batic, Omar Forrest, Marek Nowakowski
TL;DR
This paper derives new indefinite integral formulas for confluent and related Heun functions using minimal parameter assumptions and a Lagrangian approach, expanding computational tools for these special functions.
Contribution
It introduces novel indefinite integral formulas for various confluent Heun functions based on minimal assumptions and a Lagrangian framework.
Findings
New integral formulas for confluent Heun functions
Extension to biconfluent, doubly confluent, and triconfluent cases
Simplified computation of derivatives of Heun functions
Abstract
We obtain some new formulae to compute the first derivative of confluent and biconfluent Heun functions under the minimal assumption of fixing only one parameter. These results together with the Lagrangian formulation of a general homogeneous linear ordinary differential equation allow to construct several new indefinite integrals for the confluent, biconfluent, doubly confluent, and triconfluent Heun functions.
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