Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3322)

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=-1/2

http://functions.wolfram.com/07.27.03.3322.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), 7/2}, {-(1/2), 3}, -z] == (1/(31185 Pi z^2)) (16 (-10 + 151 z + 11628 z^2 + 246883 z^3 - 487528 z^4 + 17280 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2]) + (1/(31185 Pi z^2)) (16 Sqrt[1 + z] (-10 + 151 z + 11628 z^2 + 246883 z^3 - 487528 z^4 + 17280 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/ (1 + Sqrt[1 + z])^2]) + (32 Sqrt[1 + z] (5 + 3822 z + 74757 z^2 - 438884 z^3 + 230400 z^4) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(31185 Pi z^2) - (1/(31185 Pi z^2)) (32 (-5 + 3973 z + 86385 z^2 - 192001 z^3 - 257128 z^4 + 17280 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])

Standard Form

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MathML Form

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</apply> </annotation-xml> </semantics> </math>

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]