Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.6863)

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=1, a₃>=1

For fixed z and a₁=-7/2, a₂=1, a₃=3/2

For fixed z and a₁=-7/2, a₂=1, a₃=3/2, b₁=7/2

http://functions.wolfram.com/07.27.03.6863.01

Input Form

HypergeometricPFQ[{-(7/2), 1, 3/2}, {7/2, 7/2}, z] == (34335 + 94955 z + 18723 z^2 - 7287 z^3 + 1820 z^4 - 210 z^5)/(49152 z^2) - (35 (-207 - 102 z + 450 z^2 - 200 z^3 + 75 z^4 - 18 z^5 + 2 z^6) Log[1 - Sqrt[z]])/(32768 z^(5/2)) + (35 (-207 - 102 z + 450 z^2 - 200 z^3 + 75 z^4 - 18 z^5 + 2 z^6) Log[1 + Sqrt[z]])/(32768 z^(5/2)) + (525 (1 + 6 z) PolyLog[2, -Sqrt[z]])/ (4096 z^(5/2)) - (525 (1 + 6 z) PolyLog[2, Sqrt[z]])/(4096 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]