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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/07.15.06.0027.01









  


  










Input Form





JacobiP[\[Nu], a, b, z] == (-((2^(a + b + \[Nu] + 1) Sin[\[Nu] Pi] Gamma[1 + b + \[Nu]])/ (Pi Gamma[-a - \[Nu]]))) (z - 1)^(-a - b - \[Nu] - 1) Sum[((Pochhammer[1 + b + \[Nu], k] Pochhammer[1 + a + b + \[Nu], k])/ (k! (a + b + 2 \[Nu] + k + 1)!)) (PolyGamma[k + 1] - PolyGamma[-b - \[Nu] - k] - PolyGamma[a + b + \[Nu] + k + 1] + PolyGamma[2 + a + b + k + 2 \[Nu]]) (2/(1 - z))^k, {k, 0, Infinity}] + ((2^(a + b + \[Nu] + 1) Gamma[a + \[Nu] + 1] Gamma[b + \[Nu] + 1] Sin[\[Nu] Pi] Sin[(a + \[Nu]) Pi])/(Pi^2 Gamma[a + b + 2 \[Nu] + 2])) (z - 1)^(-a - b - \[Nu] - 1) Log[(z - 1)/2] Hypergeometric2F1[ 1 + a + b + \[Nu], 1 + b + \[Nu], 2 + a + b + 2 \[Nu], 2/(1 - z)] + (Pochhammer[1 + a + b + \[Nu], \[Nu]]/(2^\[Nu] Gamma[1 + \[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]}] /; Element[a + b + 2 \[Nu] + 1, Integers] && a + b + 2 \[Nu] + 1 >= 0 && !Element[a + \[Nu], Integers] && Abs[1 - z] > 2










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> b </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <ci> &#957; </ci> <pi /> </apply> </apply> <apply> <sin /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> &#957; </ci> </apply> <pi /> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> log </ci> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; 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Rule Form





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





2001-10-29





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