Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6598)

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=1/2, a₃>=1/2

For fixed z and a₁=-7/2, a₂=1/2, a₃=4

For fixed z and a₁=-7/2, a₂=1/2, a₃=4, b₁=3

http://functions.wolfram.com/07.27.03.6598.01

Input Form

HypergeometricPFQ[{-(7/2), 1/2, 4}, {3, 3}, -z] == (8 (-140 - 2275 z + 9078 z^2 + 7037 z^3 + 3232 z^4 + 624 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(31185 Pi z^2) + (1/(31185 Pi z^2)) (8 Sqrt[1 + z] (-140 - 2275 z + 9078 z^2 + 7037 z^3 + 3232 z^4 + 624 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (16 Sqrt[1 + z] (70 + 8925 z + 3336 z^2 + 1577 z^3 + 312 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(31185 Pi z^2) - (32 (-35 + 3325 z + 6207 z^2 + 4307 z^3 + 1772 z^4 + 312 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(31185 Pi z^2)

Standard Form

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MathML Form

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</apply> <apply> <ci> EllipticE </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 31185 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 624 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> 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type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 31185 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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]