Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1298)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

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

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=-1/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=-1/2, b₁=2

http://functions.wolfram.com/07.27.03.1298.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), -(1/2)}, {2, 2}, z] == (1/(2679075 Pi^2 z)) (32 (-54110 + 5045861 z - 2004210 z^2 - 303298 z^3 - 11342 z^4) EllipticE[1/2 - Sqrt[1 - z]/2]^2) + (1/(2679075 Pi^2 z)) (32 Sqrt[1 - z] (43085 - 2792526 z + 651456 z^2 + 87727 z^3 + 2520 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(2679075 Pi^2 z)) (32 (54110 - 5045861 z + 2004210 z^2 + 303298 z^3 + 11342 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(2679075 Pi^2 z)) (16 (-43085 + 3481081 z - 2592774 z^2 - 173758 z^3 - 6301 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(2679075 Pi^2 z)) (16 Sqrt[1 - z] (-43085 + 2792526 z - 651456 z^2 - 87727 z^3 - 2520 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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</apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2679075 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -6301 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 173758 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2592774 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3481081 </cn> <ci> z </ci> </apply> <cn type='integer'> -43085 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2679075 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -2520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 87727 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 651456 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2792526 </cn> <ci> z </ci> </apply> <cn type='integer'> -43085 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2679075 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

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

2007-05-02

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]