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variants of this functions
Hypergeometric2F1Regularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Series representations > Generalized power series > Expansions at z==1 > For the function itself > Logarithmic cases





http://functions.wolfram.com/07.24.06.0017.01









  


  










Input Form





Hypergeometric2F1Regularized[a, b, a + b + n, z] == (-(1/(Gamma[a] Gamma[b] n!))) (z - 1)^n Log[1 - z] Hypergeometric2F1[a + n, b + n, 1 + n, 1 - z] + ((n - 1)!/(Gamma[a + n] Gamma[b + n])) Sum[((Pochhammer[a, k] Pochhammer[b, k])/(k! Pochhammer[1 - n, k])) (1 - z)^k, {k, 0, n - 1}] + (1/(Gamma[a] Gamma[b])) (z - 1)^n Sum[((Pochhammer[a + n, k] Pochhammer[b + n, k])/(k! (n + k)!)) (PolyGamma[k + 1] + PolyGamma[k + n + 1] - PolyGamma[a + n + k] - PolyGamma[b + n + k]) (1 - z)^k, {k, 0, Infinity}] /; Element[n, Integers] && n > 0 && Abs[1 - z] < 1










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <lt /> <apply> <abs /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





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