Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1417)

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=1/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=1/2, b₁=4

http://functions.wolfram.com/07.27.03.1417.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 1/2}, {4, 4}, z] == (1/(870463318725 Pi^2 z^3)) (2048 (-11839702 - 479236219 z - 4681596367 z^2 + 8752938487 z^3 + 2957196535 z^4 + 378111259 z^5 + 10096836 z^6) EllipticE[1/2 - Sqrt[1 - z]/2]^2) - (1/(870463318725 Pi^2 z^3)) (2048 Sqrt[1 - z] (-9317182 - 347714297 z - 3224755590 z^2 + 3135899647 z^3 + 965237648 z^4 + 105133341 z^5 + 2162160 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) - (1/(870463318725 Pi^2 z^3)) (2048 (-11839702 - 479236219 z - 4681596367 z^2 + 8752938487 z^3 + 2957196535 z^4 + 378111259 z^5 + 10096836 z^6) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2]) + (1/(870463318725 Pi^2 z^3)) (1024 Sqrt[1 - z] (-9317182 - 347714297 z - 3224755590 z^2 + 3135899647 z^3 + 965237648 z^4 + 105133341 z^5 + 2162160 z^6) EllipticK[1/2 - Sqrt[1 - z]/2]^2) + (1/(870463318725 Pi^2 z^3)) (2048 (-4658591 - 171843168 z - 1541793148 z^2 + 3895061831 z^3 + 862199916 z^4 + 107751232 z^5 + 2794479 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]