Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ac7z)

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=2, a₃>=2

For fixed z and a₁=-5/2, a₂=2, a₃=2

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

http://functions.wolfram.com/07.27.03.ac7z.01

Input Form

HypergeometricPFQ[{-(5/2), 2, 2}, {-(3/2), 7/2}, -z] == (-69120 - 2880 z + 4704 z^2 - 9800 z^3 + 44100 z^4 + 11025 Pi^2 z^(9/2))/ (12288 z^2) + (1/(49152 (1 + z)^(17/2))) ((386304 + 9026944 z + 144931360 z^2 - 710360520 z^3 + 205942240 z^4 - 222903071 z^5 - 339397326 z^6 - 375507750 z^7 - 272541900 z^8 - 125576775 z^9 - 33436110 z^10 - 3928260 z^11) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(49152 (1 + z)^(17/2))) ((-386304 - 9026944 z - 144931360 z^2 + 710360520 z^3 - 205942240 z^4 + 222903071 z^5 + 339397326 z^6 + 375507750 z^7 + 272541900 z^8 + 125576775 z^9 + 33436110 z^10 + 3928260 z^11) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (5 Sqrt[1 + z] (1152 - 336 z + 392 z^2 - 490 z^3 + 735 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/(1024 z^(5/2)) + (1/(49152 (1 + z)^(17/2))) ((-386304 - 9026944 z - 144931360 z^2 + 710360520 z^3 - 205942240 z^4 + 222903071 z^5 + 339397326 z^6 + 375507750 z^7 + 272541900 z^8 + 125576775 z^9 + 33436110 z^10 + 3928260 z^11) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) + (3675 z^(5/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/1024 + (3675 z^(5/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/1024 - (3675 z^(5/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/1024

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]