Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.4725)

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=-1/2

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

http://functions.wolfram.com/07.27.03.4725.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), -(1/2)}, {1/2, 7/2}, z] == (175 Pi^2 Sqrt[-z])/3072 + (Sqrt[1 - z] (-105 + 1820 z + 258316 z^2 - 24240 z^3 + 1952 z^4 - 128 z^5))/ (294912 z^2) - (35 (-1 + 18 z - 360 z^2 - 1920 z^3) Log[Sqrt[1 - z] + Sqrt[-z]])/(98304 (-z)^(5/2)) - (175/512) Sqrt[-z] Log[Sqrt[1 - z] + Sqrt[-z]]^2 + (175/256) Sqrt[-z] Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]] + (175/256) Sqrt[-z] PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]] - (175/256) Sqrt[-z] PolyLog[2, 1 - Sqrt[1 - z] - 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]