Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.5188)

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=2

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

http://functions.wolfram.com/07.27.03.5188.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), 2}, {3, 3}, z] == 64/(1485 z^2) + (64 (-20177 + 44332 z + 279738 z^2 + 29620 z^3 - 4145 z^4 + 360 z^5) EllipticE[z])/(5145525 Pi z^2) + (64 (13247 - 52688 z - 97494 z^2 + 135020 z^3 + 2095 z^4 - 180 z^5) EllipticK[z])/(5145525 Pi z^2)

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]