Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.adc9)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=7/2, a₃>=7/2

For fixed z and a₁=-5/2, a₂=7/2, a₃=7/2

For fixed z and a₁=-5/2, a₂=7/2, a₃=7/2, b₁=-3/2

http://functions.wolfram.com/07.27.03.adc9.01

Input Form

HypergeometricPFQ[{-(5/2), 7/2, 7/2}, {-(3/2), 4}, z] == (1/(10395 Pi (-1 + z)^2 z^3)) (32 (504 - 959 z + 569 z^2 + 1316 z^3 + 4352 z^4 + 41984 z^5 - 114688 z^6 + 65536 z^7) EllipticE[z]) - (32 (-504 + 707 z - 310 z^2 - 736 z^3 - 2560 z^4 - 28672 z^5 + 32768 z^6) EllipticK[z])/(10395 Pi (-1 + z) z^3)

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]