Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2887)

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=-5/2, a₃>=-5/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=3/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=3/2, b₁=4

http://functions.wolfram.com/07.27.03.2887.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 3/2}, {4, 4}, z] == (1/(66958716825 Pi^2 z^3)) (2048 (7957970 + 153585220 z + 303777465 z^2 + 1012794319 z^3 + 519289268 z^4 + 54456294 z^5 + 190080 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) - (1/(66958716825 Pi^2 z^3)) (2048 Sqrt[1 - z] (6156170 + 106363050 z + 169311240 z^2 + 402588799 z^3 + 170518254 z^4 + 14006520 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(66958716825 Pi^2 z^3)) (2048 (7957970 + 153585220 z + 303777465 z^2 + 1012794319 z^3 + 519289268 z^4 + 54456294 z^5 + 190080 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(66958716825 Pi^2 z^3)) (1024 Sqrt[1 - z] (6156170 + 106363050 z + 169311240 z^2 + 402588799 z^3 + 170518254 z^4 + 14006520 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(66958716825 Pi^2 z^3)) (1024 (6156170 + 103735415 z + 127813260 z^2 + 611577259 z^3 + 302993722 z^4 + 30735717 z^5 + 95040 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^ 2)

Standard Form

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MathML Form

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type='integer'> 6156170 </cn> </apply> <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> <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> </apply> </apply> <apply> <times 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<times /> <cn type='integer'> 66958716825 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 95040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 30735717 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 302993722 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 611577259 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 127813260 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 103735415 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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]