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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/07.23.06.0048.01









  


  










Input Form





Hypergeometric2F1[a, b, c, z] == Subscript[F, Infinity][z, a, b, c] /; Subscript[F, n][z, a, b, c] == Sum[(Pochhammer[a, k] Pochhammer[b, k] z^k)/ (Pochhammer[c, k] k!), {k, 0, n}] == Hypergeometric2F1[a, b, c, z] - ((z^(n + 1) Pochhammer[a, n + 1] Pochhammer[b, n + 1])/ ((n + 1)! Pochhammer[c, n + 1])) HypergeometricPFQ[ {1, n + a + 1, n + b + 1}, {n + 2, n + c + 1}, z] && Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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Rule Form





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2007-05-02





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