Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av6d)

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=-3/2

http://functions.wolfram.com/07.27.03.av6d.01

Input Form

HypergeometricPFQ[{7/2, 7/2, 7/2}, {-(3/2), 2}, z] == (1/(225 Pi (-1 + z)^10 z)) (4 (-9 + 399 z - 7914 z^2 + 238950 z^3 + 1621275 z^4 + 1820107 z^5 + 440568 z^6 + 15392 z^7) EllipticE[z]) + (1/(225 Pi (-1 + z)^9 z)) (4 (-9 + 282 z - 5070 z^2 + 167160 z^3 + 906735 z^4 + 833062 z^5 + 158384 z^6 + 3840 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]