Fractional Integral and Generalized Stieltjes Transforms for Hypergeometric Functions as Transmutation Operators

Symmetry Integrability and Geometry-Methods and Applications

article

Tom H. Koornwinder¹ 

[1] Korteweg-de Vries Institute, University of Amsterdam

关键词: Gauss hypergeometric function;    Euler integral representation;    fractional integral transform;    Stieltjes transform;    transmutation formula;   

DOI  :  10.3842/SIGMA.2015.074

来源: National Academy of Science of Ukraine

【 摘 要 】

For each of the eight $n$-th derivative parameter changing formulas for Gauss hypergeometric functions a corresponding fractional integration formula is given. For both types of formulas the differential or integral operator is intertwining between two actions of the hypergeometric differential operator (for two sets of parameters): a so-called transmutation property. This leads to eight fractional integration formulas and four generalized Stieltjes transform formulas for each of the six different explicit solutions of the hypergeometric differential equation, by letting the transforms act on the solutions. By specialization two Euler type integral representations for each of the six solutions are obtained.

【 授权许可】

Unknown