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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > Specialized values > For fixed b, z





http://functions.wolfram.com/07.23.03.0146.01









  


  








Input Form





Hypergeometric2F1[n, b, m, z] == (((m - 1)! Gamma[b - m + n])/((n - 1)! Gamma[b])) (1 - z)^(m - n - b) z^(n - m) Sum[((Pochhammer[1 - n, k] Pochhammer[m - n, k])/ (Pochhammer[1 - b + m - n, k] k!)) ((z - 1)/z)^k, {k, 0, n - 1}] + ((((m - 1)! Gamma[-b + m - n])/((m - n - 1)! Gamma[-b + m])) Sum[((Pochhammer[1 - m + n, k] Pochhammer[n, k])/ (Pochhammer[1 + b - m + n, k] k!)) ((z - 1)/z)^k, {k, 0, m - n - 1}])/ z^n /; Element[m, Integers] && m > 0 && Element[n, Integers] && n >= 0 && m > n








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