Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6029)

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=-5/2

http://functions.wolfram.com/07.27.03.6029.01

Input Form

HypergeometricPFQ[{-(7/2), 1/2, 2}, {-(5/2), -(1/2)}, -z] == (5 + 24 z - 72 z^2 + 504 z^3 + 1575 z^4 + 945 z^5)/(5 (1 + z)^2) + 189 z^(7/2) ArcTan[Sqrt[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]