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

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=-3/2, a₃>=-3/2

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

For fixed z and a₁=-3/2, a₂=-3/2, a₃=1, b₁=5/2

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

Input Form

HypergeometricPFQ[{-(3/2), -(3/2), 1}, {5/2, 4}, z] == -((2 (-8 + 324 z + 3969 z^2))/(11025 z^3)) + (Sqrt[1 - z] (-256 + 10240 z + 99021 z^2 + 102592 z^3 + 13628 z^4))/ (176400 z^3) + ((105 + 378 z + 216 z^2 + 16 z^3) ArcSin[Sqrt[z]])/ (560 z^(3/2))

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]