Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.4959)

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=-1/2, a₃>=-1/2

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

For fixed z and a₁=-7/2, a₂=-1/2, a₃=1, b₁=3

http://functions.wolfram.com/07.27.03.4959.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), 1}, {3, 4}, z] == -((8 (8 + 55 z))/(495 z^2)) + (256 (495 + 65699 z + 300486 z^2 + 215134 z^3 + 8675 z^4 - 705 z^5 + 40 z^6) EllipticE[z])/(22297275 Pi z^3) - (1/(22297275 Pi z^3)) (256 (495 + 42929 z + 118394 z^2 - 72958 z^3 - 88525 z^4 - 355 z^5 + 20 z^6) 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]