Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1647)

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=3/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=3/2, b₁=2

http://functions.wolfram.com/07.27.03.1647.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 3/2}, {2, 2}, z] == (1/(893025 Pi^2 z)) (32 (39410 + 1463122 z + 4056426 z^2 + 2134801 z^3 + 169712 z^4) EllipticE[1/2 - Sqrt[1 - z]/2]^2) + (1/(893025 Pi^2 z)) (32 (-39410 - 1463122 z - 4056426 z^2 - 2134801 z^3 - 169712 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(893025 Pi^2 z)) (32 Sqrt[1 - z] (-28385 - 719022 z - 1631394 z^2 - 692152 z^3 - 40320 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(893025 Pi^2 z)) (16 Sqrt[1 - z] (28385 + 719022 z + 1631394 z^2 + 692152 z^3 + 40320 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(893025 Pi^2 z)) (16 (28385 + 930842 z + 2455128 z^2 + 1242907 z^3 + 94936 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> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 893025 </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'> 94936 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1242907 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2455128 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 930842 </cn> <ci> z </ci> </apply> <cn type='integer'> 28385 </cn> </apply> <apply> <power 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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]