Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.av9t)

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=4

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

http://functions.wolfram.com/07.27.03.av9t.01

Input Form

HypergeometricPFQ[{7/2, 7/2, 4}, {1, 1}, -z] == ((956 - 25609 z + 99236 z^2 - 86790 z^3 + 16440 z^4 - 345 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/(120 Pi (1 + z)^9) + ((956 - 25609 z + 99236 z^2 - 86790 z^3 + 16440 z^4 - 345 z^5) EllipticE[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (120 Pi (1 + z)^(17/2)) + ((-120 + 4651 z - 22888 z^2 + 24150 z^3 - 5400 z^4 + 135 z^5) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])/ (30 Pi z (1 + z)^8) + (1/(60 Pi z (1 + z)^(17/2))) ((240 - 10018 z + 62083 z^2 - 101760 z^3 + 49290 z^4 - 5910 z^5 + 75 z^6) EllipticK[(-1 + Sqrt[1 + z])^2/(1 + Sqrt[1 + z])^2])

Standard Form

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MathML Form

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<ci> z </ci> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]