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

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=1, a₃>=1

For fixed z and a₁=-3/2, a₂=1, a₃=4

For fixed z and a₁=-3/2, a₂=1, a₃=4, b₁=-1/2

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

Input Form

HypergeometricPFQ[{-(3/2), 1, 4}, {-(1/2), 1/2}, -z] == (1/(128 (1 + z)^3)) (128 - 2268 z - 945 Pi^2 z^(3/2) - 9236 z^2 - 2835 Pi^2 z^(5/2) - 10500 z^3 - 2835 Pi^2 z^(7/2) - 3780 z^4 - 945 Pi^2 z^(9/2)) + (1/(1024 (1 + z)^(13/2))) ((-1024 + 31360 z + 352160 z^2 + 1418080 z^3 + 2852468 z^4 + 3282853 z^5 + 2202903 z^6 + 805752 z^7 + 124608 z^8) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(1024 (1 + z)^(13/2))) ((1024 - 31360 z - 352160 z^2 - 1418080 z^3 - 2852468 z^4 - 3282853 z^5 - 2202903 z^6 - 805752 z^7 - 124608 z^8) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (3 (35 Sqrt[z] + 528 z^(3/2) + 1218 z^(5/2) + 1050 z^(7/2) + 315 z^(9/2)) Log[Sqrt[z] + Sqrt[1 + z]])/(32 (1 + z)^(7/2)) + (1/(1024 (1 + z)^(13/2))) ((1024 - 31360 z - 352160 z^2 - 1418080 z^3 - 2852468 z^4 - 3282853 z^5 - 2202903 z^6 - 805752 z^7 - 124608 z^8) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) - (945/32) z^(3/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] - (945/32) z^(3/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] + (945/32) z^(3/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]

Standard Form

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MathML 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]