Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ac8h)

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=-1/2

http://functions.wolfram.com/07.27.03.ac8h.01

Input Form

HypergeometricPFQ[{-(5/2), 2, 2}, {-(1/2), 7/2}, -z] == (-17280 - 1920 z + 5296 z^2 - 35200 z^3 - 11250 Pi^2 z^(7/2) - 44100 z^4 - 11025 Pi^2 z^(9/2))/(8192 z^2) + (1/(16384 (1 + z)^(15/2))) ((128768 + 6709120 z - 37675440 z^2 + 60698720 z^3 + 103843360 z^4 + 179118153 z^5 + 195678150 z^6 + 139851150 z^7 + 63422100 z^8 + 16615425 z^9 + 1920030 z^10) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(16384 (1 + z)^(15/2))) ((-128768 - 6709120 z + 37675440 z^2 - 60698720 z^3 - 103843360 z^4 - 179118153 z^5 - 195678150 z^6 - 139851150 z^7 - 63422100 z^8 - 16615425 z^9 - 1920030 z^10) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (15 Sqrt[1 + z] (-288 + 64 z - 108 z^2 + 260 z^3 + 735 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/(2048 z^(5/2)) + (1/(16384 (1 + z)^(15/2))) ((-128768 - 6709120 z + 37675440 z^2 - 60698720 z^3 - 103843360 z^4 - 179118153 z^5 - 195678150 z^6 - 139851150 z^7 - 63422100 z^8 - 16615425 z^9 - 1920030 z^10) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) - (225 z^(3/2) (50 + 49 z) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/2048 - (225 z^(3/2) (50 + 49 z) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/2048 + (225 z^(3/2) (50 + 49 z) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/2048

Standard Form

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MathML Form

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103843360 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 60698720 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 37675440 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6709120 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 128768 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 16384 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> 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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]