Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1040)

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

http://functions.wolfram.com/07.27.03.1040.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {3, 3}, z] == -((1/(39224337075 Pi^2 z^2)) (512 (415135 + 58710540 z - 5079129952 z^2 + 13672026374 z^3 - 3658024236 z^4 + 66172408 z^5) EllipticE[1/2 - Sqrt[1 - z]/2]^2)) + (1/(39224337075 Pi^2 z^2)) (512 Sqrt[1 - z] (334285 + 45322480 z - 2908541952 z^2 + 6756194036 z^3 - 1535176372 z^4 + 21741720 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(39224337075 Pi^2 z^2)) (512 (415135 + 58710540 z - 5079129952 z^2 + 13672026374 z^3 - 3658024236 z^4 + 66172408 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(39224337075 Pi^2 z^2)) (256 Sqrt[1 - z] (-334285 - 45322480 z + 2908541952 z^2 - 6756194036 z^3 + 1535176372 z^4 - 21741720 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(39224337075 Pi^2 z^2)) (256 (-334285 - 45175550 z + 3540743732 z^2 - 10663225112 z^3 + 4946434652 z^4 - 462741584 z^5 + 4002075 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]