Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av5l)

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=7/2

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

http://functions.wolfram.com/07.27.03.av5l.01

Input Form

HypergeometricPFQ[{7/2, 7/2, 7/2}, {-(7/2), 2}, -z] == (1/(2625 Pi z (1 + z)^12)) (4 (189 + 5402 z + 67691 z^2 + 572792 z^3 + 4494499 z^4 + 72811522 z^5 - 288634859 z^6 + 211579148 z^7 - 35616064 z^8 + 895232 z^9) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (1/(2625 Pi z (1 + z)^(23/2))) (4 (189 + 5402 z + 67691 z^2 + 572792 z^3 + 4494499 z^4 + 72811522 z^5 - 288634859 z^6 + 211579148 z^7 - 35616064 z^8 + 895232 z^9) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (1/(2625 Pi z (1 + z)^11)) (8 (1407 + 25423 z + 246530 z^2 + 1956894 z^3 + 24226355 z^4 - 136169789 z^5 + 120004284 z^6 - 23430080 z^7 + 680192 z^8) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) - (1/(2625 Pi z (1 + z)^(23/2))) (16 (-609 - 10714 z - 102131 z^2 - 815316 z^3 - 10844375 z^4 + 92377478 z^5 - 136234677 z^6 + 57502472 z^7 - 6433088 z^8 + 107520 z^9) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])

Standard Form

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MathML Form

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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> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2625 </cn> <pi /> <ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 23 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 107520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 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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]