Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.1027)

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=1/2

http://functions.wolfram.com/07.27.03.1027.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {1/2, 7/2}, z] == (1225 Sqrt[-z] (350 Pi^2 - 1575 Pi^2 z + 504 Pi^2 z^2 - 8 Pi^2 z^3))/ 1572864 + (1/(1207959552 z^2)) (Sqrt[1 - z] (-5145 + 367010 z + 1161898768 z^2 - 21777544032 z^3 + 17606914240 z^4 - 743337856 z^5)) - (1/(402653184 (-z)^(5/2))) (35 (-49 + 3528 z - 441000 z^2 + 31360000 z^3 + 105840000 z^4 - 104315904 z^5 + 3283968 z^6) Log[Sqrt[1 - z] + Sqrt[-z]]) - (1225 Sqrt[-z] (350 - 1575 z + 504 z^2 - 8 z^3) Log[Sqrt[1 - z] + Sqrt[-z]]^ 2)/262144 + (1225 Sqrt[-z] (350 - 1575 z + 504 z^2 - 8 z^3) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/131072 + (1225 Sqrt[-z] (350 - 1575 z + 504 z^2 - 8 z^3) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/131072 - (1225 Sqrt[-z] (350 - 1575 z + 504 z^2 - 8 z^3) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/131072

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]