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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2},{b1,b2},z] > Identities > Recurrence identities > Consecutive neighbors





http://functions.wolfram.com/07.25.17.0003.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {b, Subscript[b, 2]}, z] == (Subscript[B, 1] + Subscript[C, 1] z) HypergeometricPFQ[ {Subscript[a, 1], Subscript[a, 2]}, {b + 1, Subscript[b, 2]}, z] + (Subscript[B, 2] + Subscript[C, 2] z) HypergeometricPFQ[ {Subscript[a, 1], Subscript[a, 2]}, {b + 2, Subscript[b, 2]}, z] + Subscript[C, 3] z HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {b + 3, Subscript[b, 2]}, z] /; Subscript[B, 1] == (2 + 2 b - Subscript[b, 2])/b && Subscript[C, 1] == 1/b && Subscript[B, 2] == (Subscript[b, 2] - b - 2)/b && Subscript[C, 2] == (Subscript[a, 1] + Subscript[a, 2] - 2 b - 3)/ (b (1 + b)) && Subscript[C, 3] == ((2 + b - Subscript[a, 1]) (2 + b - Subscript[a, 2]))/(b (1 + b) (2 + b))










Standard Form





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MathML Form







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<apply> <power /> <apply> <times /> <ci> b </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </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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