Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.5649)

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=-1/2, a₃>=-1/2

For fixed z and a₁=-7/2, a₂=-1/2, a₃=4

For fixed z and a₁=-7/2, a₂=-1/2, a₃=4, b₁=3/2

http://functions.wolfram.com/07.27.03.5649.01

Input Form

HypergeometricPFQ[{-(7/2), -(1/2), 4}, {3/2, 5/2}, z] == (210 + 252675 z + 196553 z^2 - 75845 z^3 + 15015 z^4)/(327680 z) + (21 (2 - 515 z - 960 z^2 + 2100 z^3 - 770 z^4 + 143 z^5) Log[1 - Sqrt[z]])/ (131072 z^(3/2)) - (21 (2 - 515 z - 960 z^2 + 2100 z^3 - 770 z^4 + 143 z^5) Log[1 + Sqrt[z]])/(131072 z^(3/2)) - (525 (1 + 14 z) PolyLog[2, -Sqrt[z]])/(16384 Sqrt[z]) + (525 (1 + 14 z) PolyLog[2, Sqrt[z]])/(16384 Sqrt[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]