Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a8f5)

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

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

http://functions.wolfram.com/07.27.03.a8f5.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3}, {7/2, 7/2}, z] == (-5265 + 45720 z + 1387156 z^2 + 1415280 z^3 + 171765 z^4)/(2097152 z^2) + (15 (-171 + 1625 z - 30000 z^2 - 18000 z^3 + 38875 z^4 + 7671 z^5) Log[1 - Sqrt[z]])/(4194304 z^(5/2)) - (15 (-171 + 1625 z - 30000 z^2 - 18000 z^3 + 38875 z^4 + 7671 z^5) Log[1 + Sqrt[z]])/(4194304 z^(5/2)) - (225 (3 - 25 z + 300 z^2 + 1500 z^3 + 875 z^4 + 63 z^5) PolyLog[2, -Sqrt[z]])/(1048576 z^(5/2)) + (225 (3 - 25 z + 300 z^2 + 1500 z^3 + 875 z^4 + 63 z^5) PolyLog[2, Sqrt[z]])/(1048576 z^(5/2))

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]