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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/07.15.06.0023.01









  


  










Input Form





JacobiP[\[Nu], a, b, z] == (Pochhammer[1 + a + b + \[Nu], \[Nu]]/(2^\[Nu] Gamma[\[Nu] + 1])) (z - 1)^\[Nu] (1 - (2 \[Nu] (-a - \[Nu]))/((-a - b - 2 \[Nu]) (1 - z)) - (2 \[Nu] (1 - \[Nu]) (-a - \[Nu]) (1 - a - \[Nu]))/ ((-a - b - 2 \[Nu]) (1 - a - b - 2 \[Nu]) (1 - z)^2) - \[Ellipsis]) - ((2^(a + b + \[Nu] + 1) Sin[\[Nu] Pi] Gamma[-a - b - 2 \[Nu] - 1] Gamma[a + \[Nu] + 1])/(Pi Gamma[-b - \[Nu]])) (z - 1)^(-a - b - \[Nu] - 1) (1 + (2 (1 + b + \[Nu]) (1 + a + b + \[Nu]))/ ((2 + a + b + 2 \[Nu]) (1 - z)) + (2 (1 + b + \[Nu]) (2 + b + \[Nu]) (1 + a + b + \[Nu]) (2 + a + b + \[Nu]))/((2 + a + b + 2 \[Nu]) (3 + a + b + 2 \[Nu]) (1 - z)^2) + \[Ellipsis]) /; Abs[(1 - z)/2] > 1 && !Element[a + b + 2 \[Nu], Integers]










Standard Form





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MathML Form







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</ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <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> <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> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> b </ci> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <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> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <gt /> <apply> <abs /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <notin /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> <integers /> </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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