Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.3593)

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=-3/2, a₃>=-3/2

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

For fixed z and a₁=-7/2, a₂=-3/2, a₃=-3/2, b₁=5/2

http://functions.wolfram.com/07.27.03.3593.01

Input Form

HypergeometricPFQ[{-(7/2), -(3/2), -(3/2)}, {5/2, 5/2}, z] == (21 (-Pi^2 - 90 Pi^2 z + 720 Pi^2 z^2 - 160 Pi^2 z^3))/(262144 (-z)^(3/2)) - (Sqrt[1 - z] (37485 - 10201360 z + 7995508 z^2 - 25056 z^3 + 288 z^4))/ (13107200 z) - (21 (237 + 16650 z + 50400 z^2 - 46400 z^3) Log[Sqrt[1 - z] + Sqrt[-z]])/(2621440 (-z)^(3/2)) - (63 (-1 - 90 z + 720 z^2 - 160 z^3) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/ (131072 (-z)^(3/2)) + (63 (-1 - 90 z + 720 z^2 - 160 z^3) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/ (65536 (-z)^(3/2)) + (63 (-1 - 90 z + 720 z^2 - 160 z^3) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/(65536 (-z)^(3/2)) - (63 (-1 - 90 z + 720 z^2 - 160 z^3) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/ (65536 (-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]