Abstract
On a class of new hypergeometric transformations
Highlights
Hypergeometric transformations are undoubtedly a fascinating field of investigation, which originates from the identities of Pfaff (1) and Euler (2)
In [10] the theory of Theta functions is used to derive hypergeometric transformation formulæ, while [11] presents an approach referring to functional identities inspired by the work of [12]
In the first volume of his Traite [5], Legendre devotes more than a half of it to the elliptic integrals of first, second and third kind, showing their properties and explaining how to compute them by series, moduli transformation and so on
Summary
Hypergeometric transformations are undoubtedly a fascinating field of investigation, which originates from the identities of Pfaff (1) and Euler (2). 2F1 a; b x = (1 − x)c−a−b 2F1 c − a; c − b x The research for such kind of transformations is under current investigations. Algebraic transformations of hypergeometric functions of modular origin, are related to the monodromy of the underlying linear differential equations. This piece of research was started by the seminal contribution of Goursat, see [6] as the Received 14 March 2018. 1 Corresponding Author c 2018 Giovanni Mingari Scarpello and Daniele Ritelli
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