Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a8db)

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=-1/2

http://functions.wolfram.com/07.27.03.a8db.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3}, {-(1/2), 3/2}, z] == (949 - 22250 z - 40875 z^2)/1024 - (75 (1 - 45 z - 249 z^2 + 293 z^3) Log[1 - Sqrt[z]])/(2048 Sqrt[z]) + (75 (1 - 45 z - 249 z^2 + 293 z^3) Log[1 + Sqrt[z]])/(2048 Sqrt[z]) + (1575/512) (5 z^(3/2) + 3 z^(5/2)) PolyLog[2, -Sqrt[z]] - (1575/512) (5 z^(3/2) + 3 z^(5/2)) PolyLog[2, 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]