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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/07.31.06.0001.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == 1 + (Product[Subscript[a, j], {j, 1, p}]/Product[Subscript[b, j], {j, 1, q}]) z + (Product[Subscript[a, j] (1 + Subscript[a, j]), {j, 1, p}]/(2 Product[Subscript[b, j] (1 + Subscript[b, j]), {j, 1, q}])) z^2 + \[Ellipsis] /; (q == p - 1 && Abs[z] < 1) || q >= p










Standard Form





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MathML Form







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</ci> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> p </ci> </apply> </list> <list> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> &#8230; </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> q </ci> </apply> </list> <ci> z </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <times /> <apply> <product /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> p </ci> </uplimit> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> </apply> <apply> <power /> <apply> <product /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> q </ci> </uplimit> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> j </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <product /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> p </ci> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> j </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <product /> <bvar> <ci> j </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> q </ci> </uplimit> <apply> <times /> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> j </ci> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> j </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> &#8230; 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Date Added to functions.wolfram.com (modification date)





2001-10-29