Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av5n)

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.av5n.01

Input Form

HypergeometricPFQ[{7/2, 7/2, 7/2}, {-(7/2), 3}, z] == -((1/(7875 Pi (-1 + z)^11 z^2)) (16 (-462 + 4683 z - 19017 z^2 + 24090 z^3 + 153216 z^4 - 1480449 z^5 + 19057831 z^6 + 47011916 z^7 + 17000000 z^8 + 823552 z^9) EllipticE[z])) - (1/(7875 Pi (-1 + z)^10 z^2)) (32 (-231 + 2226 z - 8931 z^2 + 15276 z^3 + 26235 z^4 - 378582 z^5 + 6137567 z^6 + 11534888 z^7 + 3207872 z^8 + 107520 z^9) EllipticK[z])

Standard Form

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MathML Form

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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]