Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2064)

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=-5/2

http://functions.wolfram.com/07.27.03.2064.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 7/2}, {-(5/2), 4}, z] == -((1/(96621525 Pi z^3)) (32 (64680 + 140385 z + 666400 z^2 - 14528555 z^3 + 46299234 z^4 - 71230304 z^5 + 110994304 z^6) EllipticE[z])) - (1/(96621525 Pi z^3)) (32 (-64680 - 108045 z - 592165 z^2 + 8833705 z^3 - 26114919 z^4 + 38948696 z^5 - 67028672 z^6 + 46126080 z^7) EllipticK[z])

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]