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variants of this functions
JacobiP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > Series representations > Generalized power series > Expansions at z==infinity





http://functions.wolfram.com/07.15.06.0037.01









  


  










Input Form





JacobiP[\[Nu], a, b, z] == (((-1)^(a + b + 2 \[Nu]) 2^(1 + a) Sin[Pi \[Nu]] Gamma[1 + a])/ (Pi (1 + a + \[Nu]) Gamma[1 - b - \[Nu]] Gamma[1 + a + b + \[Nu]])) (z - 1)^(-1 - a) HypergeometricPFQ[{1, 1, 1 + a}, {1 - b - \[Nu], 2 + a + \[Nu]}, 2/(1 - z)] - ((2^(1 + a + b + \[Nu]) Sin[Pi \[Nu]] Gamma[-1 - a - b - 2 \[Nu]] Gamma[1 + a + \[Nu]])/(Pi Gamma[-b - \[Nu]])) (z - 1)^(-1 - a - b - \[Nu]) Sum[((Pochhammer[b + \[Nu] + 1, k] Pochhammer[a + b + \[Nu] + 1, k])/ (k! Pochhammer[a + b + 2 \[Nu] + 2, k])) (2/(1 - z))^k, {k, 0, -a - b - 2 \[Nu] - 2}] + (((-1)^(a + b + 2 \[Nu] - 1) (z - 1)^\[Nu])/ (2^\[Nu] (Gamma[1 + \[Nu]] Gamma[1 + a + b + \[Nu]]))) Sum[((Pochhammer[-a - \[Nu], k] Pochhammer[-\[Nu], k])/ (k! (k - 1 - a - b - 2 \[Nu])!)) (Log[(z - 1)/2] + PolyGamma[1 + k] + PolyGamma[-a - b + k - 2 \[Nu]] - PolyGamma[k - \[Nu]] - PolyGamma[1 + a - k + \[Nu]]) (2/(1 - z))^k, {k, 0, a + \[Nu]}] /; Element[-1 - a - b - 2 \[Nu], Integers] && -1 - a - b - 2 \[Nu] > 0 && Element[-b - \[Nu], Integers] && -b - \[Nu] > 0 && a + \[Nu] >= -1 && !IntervalMemberQ[Interval[{-1, 1}], z]










Standard Form





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MathML Form







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





2001-10-29





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