Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.7889)

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=-1/2

http://functions.wolfram.com/07.27.03.7889.01

Input Form

HypergeometricPFQ[{-(7/2), 3/2, 7/2}, {-(1/2), 4}, z] == (1/(45045 Pi z^3)) (32 (1960 + 1855 z + 1743 z^2 + 7120 z^3 + 78976 z^4 - 242688 z^5 + 147456 z^6) EllipticE[z]) - (32 (1960 + 875 z + 693 z^2 + 3256 z^3 + 50048 z^4 - 130560 z^5 + 73728 z^6) EllipticK[z])/(45045 Pi z^3)

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]