Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3917)

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=1

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

http://functions.wolfram.com/07.27.03.3917.01

Input Form

HypergeometricPFQ[{-(7/2), -(3/2), 1}, {4, 4}, z] == -((4 (64 + 1872 z + 9009 z^2))/(45045 z^3)) - (1/(2029052025 Pi z^3)) (1024 (-84289 - 1698238 z - 6036291 z^2 - 5445748 z^3 - 1140439 z^4 - 13230 z^5 + 315 z^6) EllipticE[z]) + (1/(2029052025 Pi z^3)) (512 (-123533 - 2005882 z - 4355931 z^2 + 1598260 z^3 + 4094861 z^4 + 791910 z^5 + 315 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]