Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1018)

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=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=-7/2, b₁=-3/2

http://functions.wolfram.com/07.27.03.1018.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {-(3/2), 7/2}, z] == (1225 (-z)^(5/2) (21 Pi^2 - Pi^2 z))/24576 + (1/(75497472 z^2)) (Sqrt[1 - z] (-5145 + 181790 z + 67900708 z^2 + 484622856 z^3 + 1622762144 z^4 - 301713728 z^5)) - (1/(25165824 (-z)^(5/2))) (35 (-49 + 1764 z - 73500 z^2 - 1568000 z^3 - 7056000 z^4 - 10612224 z^5 + 1462784 z^6) Log[Sqrt[1 - z] + Sqrt[-z]]) - (1225 (21 - z) (-z)^(5/2) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/4096 + (1225 (21 - z) (-z)^(5/2) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/2048 + (1225 (21 - z) (-z)^(5/2) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/2048 - (1225 (21 - z) (-z)^(5/2) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/2048

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]