Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a7sq)

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=-5/2, a₃>=-5/2

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

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

http://functions.wolfram.com/07.27.03.a7sq.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), -(3/2)}, {5/2, 7/2}, z] == (375 (-Pi^2 - 48 Pi^2 z + 288 Pi^2 z^2 - 64 Pi^2 z^3))/ (2097152 (-z)^(3/2)) + (Sqrt[1 - z] (-135 - 45090 z + 6344536 z^2 - 4335472 z^3 + 42816 z^4))/(8388608 z^2) - (15 (-9 - 1800 z - 76800 z^2 - 230400 z^3 + 176000 z^4 - 768 z^5) Log[Sqrt[1 - z] + Sqrt[-z]])/(8388608 (-z)^(5/2)) - (1125 (-1 - 48 z + 288 z^2 - 64 z^3) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/ (1048576 (-z)^(3/2)) + (1125 (-1 - 48 z + 288 z^2 - 64 z^3) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/ (524288 (-z)^(3/2)) + (1125 (-1 - 48 z + 288 z^2 - 64 z^3) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/(524288 (-z)^(3/2)) - (1125 (-1 - 48 z + 288 z^2 - 64 z^3) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/(524288 (-z)^(3/2))

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]