Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a880)

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=2

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

http://functions.wolfram.com/07.27.03.a880.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 2}, {5/2, 5/2}, z] == (1875 + 90697 z + 122375 z^2 + 18525 z^3)/(131072 z) + (75 (13 - 352 z - 432 z^2 + 608 z^3 + 163 z^4) Log[1 - Sqrt[z]])/ (262144 z^(3/2)) - (75 (13 - 352 z - 432 z^2 + 608 z^3 + 163 z^4) Log[1 + Sqrt[z]])/(262144 z^(3/2)) - (225 (-1 + 16 z + 108 z^2 + 80 z^3 + 7 z^4) PolyLog[2, -Sqrt[z]])/ (65536 z^(3/2)) + (225 (-1 + 16 z + 108 z^2 + 80 z^3 + 7 z^4) PolyLog[2, Sqrt[z]])/(65536 z^(3/2))

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]