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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/07.15.06.0032.01









  


  










Input Form





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