Generalized hypergeometric function 3F2: Identities (formula 07.27.17.0004)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]

Identities

Recurrence identities

Consecutive neighbors

http://functions.wolfram.com/07.27.17.0004.01

Input Form

HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {b, Subscript[b, 2]}, z] == ((Subscript[B, 1] + Subscript[C, 1] z)/z) HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {b - 1, Subscript[b, 2]}, z] + ((Subscript[B, 2] + Subscript[C, 2] z)/z) HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {b - 2, Subscript[b, 2]}, z] + ((Subscript[B, 3] + Subscript[C, 3] z)/z) HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {b - 3, Subscript[b, 2]}, z] /; Subscript[B, 1] == ((b - 1) (b - 2) (b - Subscript[b, 2] - 1))/ ((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[C, 1] == ((b - 1) ((2 b - 3) (Subscript[a, 1] + Subscript[a, 2] + Subscript[a, 3]) - Subscript[a, 1] Subscript[a, 2] - Subscript[a, 1] Subscript[a, 3] - Subscript[a, 2] Subscript[a, 3] - 7 + 9 b - 3 b^2))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[B, 2] == ((b - 1) (b - 2) (4 - 2 b + Subscript[b, 2]))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[C, 2] == ((b - 1) (b - 2) (3 b - 6 - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3]))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[B, 3] == ((b - 1) (b - 2) (b - 3))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)) && Subscript[C, 3] == -(((b - 1) (b - 2) (b - 3))/((1 + Subscript[a, 1] - b) (1 + Subscript[a, 2] - b) (1 + Subscript[a, 3] - b)))

Standard Form

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MathML Form

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</mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> B </mi> <mn> 2 </mn> </msub> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <msub> <mi> b </mi> <mn> 2 </mn> </msub> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> C </mi> <mn> 2 </mn> </msub> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> <mo> - </mo> <mn> 6 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> B </mi> <mn> 3 </mn> </msub> <mo> ⩵ </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> <mo> ∧ </mo> <mrow> <msub> <mi> C </mi> <mn> 3 </mn> </msub> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msub> <mi> a </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <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> </list> <list> <ci> b </ci> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> B </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> C </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <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> </list> <list> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </list> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> B </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> C </ci> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <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> </list> <list> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </list> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> B </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <apply> <ci> Subscript </ci> <ci> C </ci> <cn type='integer'> 3 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <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> </list> <list> <apply> <plus /> <ci> b </ci> <cn type='integer'> -3 </cn> </apply> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </list> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> B </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> C </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <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 /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </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'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> -7 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> B </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> C </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -6 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> B </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> C </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 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Rule Form

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

2001-10-29

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]