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

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=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=3

For fixed z and a₁=-5/2, a₂=1, a₃=3, b₁=-1/2

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

Input Form

HypergeometricPFQ[{-(5/2), 1, 3}, {-(1/2), 3/2}, -z] == -((7 (-112 + 1200 z + 450 Pi^2 z^(3/2) + 2700 z^2 + 675 Pi^2 z^(5/2)))/ 1024) + (1/(6144 (1 + z)^(11/2))) ((-6144 + 57888 z + 851808 z^2 + 3649436 z^3 + 7805810 z^4 + 9519705 z^5 + 6752640 z^6 + 2604675 z^7 + 423810 z^8) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(6144 (1 + z)^(11/2))) ((6144 - 57888 z - 851808 z^2 - 3649436 z^3 - 7805810 z^4 - 9519705 z^5 - 6752640 z^6 - 2604675 z^7 - 423810 z^8) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (15 (-4 + 28 z + 315 z^2 + 315 z^3) Log[Sqrt[z] + Sqrt[1 + z]])/ (256 Sqrt[z] Sqrt[1 + z]) + (1/(6144 (1 + z)^(11/2))) ((6144 - 57888 z - 851808 z^2 - 3649436 z^3 - 7805810 z^4 - 9519705 z^5 - 6752640 z^6 - 2604675 z^7 - 423810 z^8) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) - (1575/256) (2 z^(3/2) + 3 z^(5/2)) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] - (1575/256) (2 z^(3/2) + 3 z^(5/2)) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] + (1575/256) (2 z^(3/2) + 3 z^(5/2)) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + 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]