Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ai7v)

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=-3/2, a₂>=-3/2

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

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

For fixed z and a₁=-3/2, a₂=7/2, a₃=7/2, b₁=-1/2

http://functions.wolfram.com/07.27.03.ai7v.01

Input Form

HypergeometricPFQ[{-(3/2), 7/2, 7/2}, {-(1/2), 1}, -z] == (1/(75 Pi (1 + z)^5)) (2 (255 - 8010 z - 57225 z^2 - 132800 z^3 - 145664 z^4 - 77824 z^5 - 16384 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(75 Pi (1 + z)^(9/2))) (2 (255 - 8010 z - 57225 z^2 - 132800 z^3 - 145664 z^4 - 77824 z^5 - 16384 z^6) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(75 Pi z (1 + z)^(9/2))) (4 (75 - 2490 z - 23565 z^2 - 59400 z^3 - 68480 z^4 - 37888 z^5 - 8192 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (1/(75 Pi z (1 + z)^4)) (4 (-75 + 2310 z + 29265 z^2 + 87360 z^3 + 113920 z^4 + 69632 z^5 + 16384 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])

Standard Form

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MathML 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]