Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a8dt)

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.a8dt.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3}, {1/2, 7/2}, z] == (3 (-30 - 135 z + 40643 z^2 + 276585 z^3 + 99705 z^4))/(131072 z^2) + (15 (-6 - 25 z - 600 z^2 - 20100 z^3 + 8350 z^4 + 12381 z^5) Log[1 - Sqrt[z]])/(262144 z^(5/2)) - (15 (-6 - 25 z - 600 z^2 - 20100 z^3 + 8350 z^4 + 12381 z^5) Log[1 + Sqrt[z]])/(262144 z^(5/2)) - (225 Sqrt[z] (150 + 350 z + 63 z^2) PolyLog[2, -Sqrt[z]])/32768 + (225 Sqrt[z] (150 + 350 z + 63 z^2) PolyLog[2, Sqrt[z]])/32768

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]