Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a9g5)

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=-3/2, a₃>=-3/2

For fixed z and a₁=-5/2, a₂=-3/2, a₃=4

For fixed z and a₁=-5/2, a₂=-3/2, a₃=4, b₁=1/2

http://functions.wolfram.com/07.27.03.a9g5.01

Input Form

HypergeometricPFQ[{-(5/2), -(3/2), 4}, {1/2, 7/2}, z] == (-15 - 155 z + 60983 z^2 + 307005 z^3 + 20790 z^4)/(65536 z^2) + (15 (-1 - 10 z - 300 z^2 - 8480 z^3 + 7405 z^4 + 1386 z^5) Log[1 - Sqrt[z]])/(131072 z^(5/2)) - (15 (-1 - 10 z - 300 z^2 - 8480 z^3 + 7405 z^4 + 1386 z^5) Log[1 + Sqrt[z]])/(131072 z^(5/2)) - (7875 Sqrt[z] (2 + 3 z) PolyLog[2, -Sqrt[z]])/16384 + (7875 Sqrt[z] (2 + 3 z) PolyLog[2, Sqrt[z]])/16384

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]