Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.9692)

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=4

http://functions.wolfram.com/07.27.03.9692.01

Input Form

HypergeometricPFQ[{-(7/2), 7/2, 7/2}, {4, 4}, z] == -((1/(10145260125 Pi^2 z^3)) (2048 (3039974 + 4781280 z + 18882997 z^2 - 157649840 z^3 + 271417344 z^4 - 187924480 z^5 + 47185920 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2)) - (1/(10145260125 Pi^2 z^3)) (4096 Sqrt[1 - z] (-258727 - 1115233 z - 6156528 z^2 + 20522368 z^3 - 19251200 z^4 + 5898240 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(10145260125 Pi^2 z^3)) (2048 (3039974 + 4781280 z + 18882997 z^2 - 157649840 z^3 + 271417344 z^4 - 187924480 z^5 + 47185920 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(10145260125 Pi^2 z^3)) (2048 Sqrt[1 - z] (-258727 - 1115233 z - 6156528 z^2 + 20522368 z^3 - 19251200 z^4 + 5898240 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) - (1/(10145260125 Pi^2 z^3)) (1024 (517454 + 2602369 z + 11917892 z^2 - 85119032 z^3 + 140936192 z^4 - 95436800 z^5 + 23592960 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]