Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.acq9)

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=5/2, a₃>=5/2

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

For fixed z and a₁=-5/2, a₂=5/2, a₃=5/2, b₁=1

http://functions.wolfram.com/07.27.03.acq9.01

Input Form

HypergeometricPFQ[{-(5/2), 5/2, 5/2}, {1, 4}, z] == (128 (-1600 + 350 z - 325 z^2 + 16264 z^3 - 33152 z^4 + 16384 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/(51975 Pi^2 z^3) + (1/(51975 Pi^2 z^3)) (128 Sqrt[1 - z] (1600 + 50 z + 525 z^2 - 5344 z^3 + 4096 z^4) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(51975 Pi^2 z^3)) (128 (1600 - 350 z + 325 z^2 - 16264 z^3 + 33152 z^4 - 16384 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (64 Sqrt[1 - z] (-1600 - 50 z - 525 z^2 + 5344 z^3 - 4096 z^4) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(51975 Pi^2 z^3) + (128 (-800 + 375 z - 175 z^2 + 4472 z^3 - 8544 z^4 + 4096 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(51975 Pi^2 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]