Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6366)

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=3

For fixed z and a₁=-7/2, a₂=1/2, a₃=3, b₁=4

http://functions.wolfram.com/07.27.03.6366.01

Input Form

HypergeometricPFQ[{-(7/2), 1/2, 3}, {4, 4}, z] == -(256/(2145 z^3)) + (1/(96621525 Pi z^3)) (128 (493417 - 653672 z + 1366542 z^2 + 1196020 z^3 - 422375 z^4 + 103500 z^5 - 11880 z^6) EllipticE[z]) + (1/(96621525 Pi z^3)) (64 (-626474 + 1710671 z - 3353232 z^2 + 1927570 z^3 + 434570 z^4 - 104985 z^5 + 11880 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]