Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ab2f)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=1

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

http://functions.wolfram.com/07.27.03.ab2f.01

Input Form

HypergeometricPFQ[{-(5/2), 1, 1}, {3/2, 4}, -z] == (18 + 123 z + 534 z^2 + 188 z^3 + 30 z^4)/(1386 z^2) + ((231 + 99 z + 33 z^2 + 5 z^3) ArcTan[Sqrt[z]])/(231 Sqrt[z]) + ((-3 - 22 z - 99 z^2) Log[1 + z])/(231 z^3)

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]