Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1415)

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=3

http://functions.wolfram.com/07.27.03.1415.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 1/2}, {3, 4}, z] == (1/(200876150475 Pi^2 z^3)) (1024 (-194040 - 83845720 z - 1552555865 z^2 + 4471897674 z^3 + 1973040859 z^4 + 311853116 z^5 + 9930516 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) - (1/(200876150475 Pi^2 z^3)) (1024 Sqrt[1 - z] (-194040 - 63398755 z - 1098313335 z^2 + 1663378254 z^3 + 663639820 z^4 + 88778541 z^5 + 2162160 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(200876150475 Pi^2 z^3)) (1024 (-194040 - 83845720 z - 1552555865 z^2 + 4471897674 z^3 + 1973040859 z^4 + 311853116 z^5 + 9930516 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(200876150475 Pi^2 z^3)) (512 Sqrt[1 - z] (-194040 - 63398755 z - 1098313335 z^2 + 1663378254 z^3 + 663639820 z^4 + 88778541 z^5 + 2162160 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(200876150475 Pi^2 z^3)) (512 (-194040 - 63301735 z - 1071719635 z^2 + 3669504369 z^3 + 1155999643 z^4 + 178279495 z^5 + 5505798 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

Standard Form

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MathML Form

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<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'> 512 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 5505798 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 178279495 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1155999643 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3669504369 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1071719635 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 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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]