Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.9063)

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=5/2, a₃>=5/2

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

For fixed z and a₁=-7/2, a₂=5/2, a₃=7/2, b₁=4

http://functions.wolfram.com/07.27.03.9063.01

Input Form

HypergeometricPFQ[{-(7/2), 5/2, 7/2}, {4, 4}, z] == -((1/(2029052025 Pi^2 z^3)) (2048 (-5562494 + 2602369 z + 5447218 z^2 - 27240424 z^3 + 34429184 z^4 - 18890752 z^5 + 3932160 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2)) - (1/(2029052025 Pi^2 z^3)) (2048 Sqrt[1 - z] (3039974 - 423458 z - 2905875 z^2 + 5792704 z^3 - 4016128 z^4 + 983040 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(2029052025 Pi^2 z^3)) (2048 (-5562494 + 2602369 z + 5447218 z^2 - 27240424 z^3 + 34429184 z^4 - 18890752 z^5 + 3932160 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(2029052025 Pi^2 z^3)) (1024 Sqrt[1 - z] (3039974 - 423458 z - 2905875 z^2 + 5792704 z^3 - 4016128 z^4 + 983040 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) - (1/(2029052025 Pi^2 z^3)) (1024 (-3039974 + 1312815 z + 3235337 z^2 - 14469652 z^3 + 17751168 z^4 - 9568256 z^5 + 1966080 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2)

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]