Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.4103)

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=2

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

http://functions.wolfram.com/07.27.03.4103.01

Input Form

HypergeometricPFQ[{-(7/2), -(3/2), 2}, {1/2, 7/2}, z] == (105 - 385 z + 29499 z^2 + 103089 z^3 + 8610 z^4 - 630 z^5)/(32768 z^2) - (105 (-1 + 4 z + 30 z^2 + 400 z^3 - 355 z^4 - 84 z^5 + 6 z^6) Log[1 - Sqrt[z]])/(65536 z^(5/2)) + (105 (-1 + 4 z + 30 z^2 + 400 z^3 - 355 z^4 - 84 z^5 + 6 z^6) Log[1 + Sqrt[z]])/(65536 z^(5/2)) - (1575 Sqrt[z] (4 + 5 z) PolyLog[2, -Sqrt[z]])/8192 + (1575 Sqrt[z] (4 + 5 z) PolyLog[2, Sqrt[z]])/8192

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]