Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a8de)

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.a8de.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), 3}, {-(1/2), 5/2}, z] == -((3 (25 - 4853 z + 68625 z^2 + 86475 z^3))/(16384 z)) - (75 (1 + 24 z - 540 z^2 - 1432 z^3 + 1947 z^4) Log[1 - Sqrt[z]])/ (32768 z^(3/2)) + (75 (1 + 24 z - 540 z^2 - 1432 z^3 + 1947 z^4) Log[1 + Sqrt[z]])/(32768 z^(3/2)) + (1575 z^(3/2) (20 + 9 z) PolyLog[2, -Sqrt[z]])/4096 - (1575 z^(3/2) (20 + 9 z) PolyLog[2, Sqrt[z]])/4096

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]