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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Identities > Functional identities > Relations including three Kummer's solutions





http://functions.wolfram.com/07.23.17.0078.01









  


  










Input Form





Hypergeometric2F1[a, b, c, z] == ((Gamma[1 - a] Gamma[1 - b])/(Gamma[1 - c] Gamma[1 - a - b + c])) (1 - 1/z)^(c - a - b) (-(1/z))^(a + b - c) (1/z)^(-b + c) Hypergeometric2F1[1 - b, -b + c, 1 - a - b + c, 1 - 1/z] + ((Gamma[1 - a] Gamma[1 - b] Gamma[c])/(Gamma[2 - c] Gamma[-a + c] Gamma[-b + c])) (1/z)^(-1 + c) Hypergeometric2F1[1 + b - c, 1 + a - c, 2 - c, z] /; !IntervalMemberQ[Interval[{1, Infinity}], z]










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998- Wolfram Research, Inc.