Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a815)

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=1

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

http://functions.wolfram.com/07.27.03.a815.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 1}, {3/2, 7/2}, z] == (45 - 1110 z + 60438 z^2 + 49810 z^3 + 5505 z^4)/(98304 z^2) + (5 (3 - 75 z - 1300 z^2 - 300 z^3 + 1425 z^4 + 247 z^5) Log[1 - Sqrt[z]])/ (65536 z^(5/2)) - (5 (3 - 75 z - 1300 z^2 - 300 z^3 + 1425 z^4 + 247 z^5) Log[1 + Sqrt[z]])/(65536 z^(5/2)) - (75 (10 + 30 z + 15 z^2 + z^3) PolyLog[2, -Sqrt[z]])/(8192 Sqrt[z]) + (75 (10 + 30 z + 15 z^2 + z^3) PolyLog[2, Sqrt[z]])/(8192 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]