Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.9612)

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=-5/2

http://functions.wolfram.com/07.27.03.9612.01

Input Form

HypergeometricPFQ[{-(7/2), 7/2, 7/2}, {-(5/2), 4}, z] == (1/(75075 Pi (-1 + z)^2 z^3)) (32 (4312 - 8183 z + 4753 z^2 + 9104 z^3 + 21056 z^4 + 69632 z^5 + 671744 z^6 - 1835008 z^7 + 1048576 z^8) EllipticE[z]) - (1/(75075 Pi (-1 + z) z^3)) (32 (-4312 + 6027 z - 2548 z^2 - 4960 z^3 - 11776 z^4 - 40960 z^5 - 458752 z^6 + 524288 z^7) 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]