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Algebraic Relations between the Hypergeometric E-Function and Its Derivatives

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Abstract

In this paper, we consider the generalized hypergeometric function

$$\sum\limits_{n = 0}^\infty {\frac{1}{{\left( {{\lambda }_{1} + 1} \right)_n ...\left( {{\lambda }_t + 1} \right)_n }}} \left( {\frac{z}{t}} \right)^{tn} ,{ \lambda }_{1} ,...,{\lambda }_{t} \in \mathbb{Q}\backslash \left\{ { - 1, - 2,...} \right\},$$

where t is an even number, and its derivatives up to the order t- 1 inclusive. In the case of algebraic dependence between these functions over \(\mathbb{C}\)(z), a complete structure of algebraic relations between them is given.

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Authors and Affiliations

  1. Bryansk Institute of Transport Engineering, Russia

    G. G. Viskina & V. Kh. Salikhov

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  1. G. G. Viskina
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  2. V. Kh. Salikhov
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Viskina, G.G., Salikhov, V.K. Algebraic Relations between the Hypergeometric E-Function and Its Derivatives. Mathematical Notes 71, 761–772 (2002). https://doi.org/10.1023/A:1015864711107

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