Abstract
The function represented by the infinite series \(\sum\limits_{n = 0}^\infty {\frac{{{{(a)}_n}{{(b)}_n}}}{{{{(c)}_n}}}\frac{{{z^n}}}{{n!}}} \) within its circle of convergence and all the analytic continuations is called the hypergeometric function 2 F 1(a, b; c;z).*
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Literature
Erdélyi, A.: Higher transcendental functions, Vol. 1. New York: McGraw-Hill 1953.
Kampé de Fériet, J.: La fonction hypergeometrique. Paris: Gauthiers-Villars 1937.
Klein, F.: Vorlesungen über die hypergeometrische Funktion. Berlin: Teubner 1933.
MacRobert, T. M.: Proc. Edinburgh Math. Soc. 42 (1923) 84–88.
MacRobert, T. M.: Functions of a complex variable. London: Macmillan 1954.
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© 1966 Springer-Verlag Berlin Heidelberg
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Magnus, W., Oberhettinger, F., Soni, R.P. (1966). The hypergeometric function. In: Formulas and Theorems for the Special Functions of Mathematical Physics. Die Grundlehren der mathematischen Wissenschaften, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-11761-3_2
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DOI: https://doi.org/10.1007/978-3-662-11761-3_2
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