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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Identities > Recurrence identities > Consecutive neighbors





http://functions.wolfram.com/07.28.17.0002.01









  


  










Input Form





HypergeometricPFQ[{a, Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == ((Subscript[B, 1] + Subscript[C, 1] z)/(z - 1)) HypergeometricPFQ[{a - 1, Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + ((Subscript[B, 2] + Subscript[C, 2] z)/(z - 1)) HypergeometricPFQ[{a - 2, Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + ((Subscript[B, 3] + Subscript[C, 3] z)/(z - 1)) HypergeometricPFQ[{a - 3, Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] + (Subscript[B, 4]/(z - 1)) HypergeometricPFQ[ {a - 4, Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] /; Subscript[B, 1] == (Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3] - 4 a + 7)/(a - 1) && Subscript[C, 1] == (Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4] - 3 a + 6)/(1 - a) && Subscript[B, 2] == ((7 - 3 a) (Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]) + Subscript[b, 1] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 3] + Subscript[b, 2] Subscript[b, 3] + 31 - 27 a + 6 a^2)/((a - 1) (a - 2)) && Subscript[C, 2] == ((2 a - 5) (Subscript[a, 2] + Subscript[a, 3] + Subscript[a, 4]) - Subscript[a, 2] Subscript[a, 3] - Subscript[a, 2] Subscript[a, 4] - Subscript[a, 3] Subscript[a, 4] - 19 + 15 a - 3 a^2)/ ((a - 1) (a - 2)) && Subscript[B, 3] == (Subscript[b, 1] Subscript[b, 2] Subscript[b, 3] + (a - 3) ((3 a - 8) (Subscript[b, 1] + Subscript[b, 2] + Subscript[b, 3]) - 2 (Subscript[b, 1] Subscript[b, 2] + Subscript[b, 1] Subscript[b, 3] + Subscript[b, 2] Subscript[b, 3]) - 28 + 21 a - 4 a^2))/((a - 1) (a - 2) (a - 3)) && Subscript[C, 3] == ((a - Subscript[a, 2] - 3) (a - Subscript[a, 3] - 3) (a - Subscript[a, 4] - 3))/((a - 1) (a - 2) (a - 3)) && Subscript[B, 4] == ((a - Subscript[b, 1] - 3) (a - Subscript[b, 2] - 3) (a - Subscript[b, 3] - 3))/((a - 1) (a - 2) (a - 3))










Standard Form





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MathML Form







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type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <cn type='integer'> -19 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> B </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='integer'> -3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> 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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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