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

Plamen P Fiziev

2009
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Journal of Physics A: Mathematical and Theoretical
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*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. ...
Then because *of* *the* obvious symmetry *of* *the* equation (1.1) under *the* change {α, β, γ, δ, µ, ν, z} → {α, γ, β, δ, ν, µ, z − 1}, *the* spectral parameter will be −ν. ...

doi:10.1088/1751-8113/43/3/035203
fatcat:n7k22uuzsbb5nlirgmrs3bq6mm