Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.7940)

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=3/2, a₃>=3/2

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

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

http://functions.wolfram.com/07.27.03.7940.01

Input Form

HypergeometricPFQ[{-(7/2), 3/2, 7/2}, {3, 4}, z] == -((1/(156080925 Pi^2 z^3)) (1024 (64680 - 899458 z + 1165633 z^2 - 3729738 z^3 + 3992704 z^4 - 2000896 z^5 + 393216 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2)) - (1/(156080925 Pi^2 z^3)) (1024 Sqrt[1 - z] (-64680 + 567973 z - 459711 z^2 + 696624 z^3 - 429568 z^4 + 98304 z^5) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(156080925 Pi^2 z^3)) (1024 (64680 - 899458 z + 1165633 z^2 - 3729738 z^3 + 3992704 z^4 - 2000896 z^5 + 393216 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(156080925 Pi^2 z^3)) (512 Sqrt[1 - z] (-64680 + 567973 z - 459711 z^2 + 696624 z^3 - 429568 z^4 + 98304 z^5) EllipticK[1/2 - Sqrt[1 - z]/2]^2) - (1/(156080925 Pi^2 z^3)) (512 (64680 - 600313 z + 658805 z^2 - 1965465 z^3 + 2053504 z^4 - 1012736 z^5 + 196608 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]