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

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=3, a₃>=3

For fixed z and a₁=-3/2, a₂=3, a₃=3

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

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

Input Form

HypergeometricPFQ[{-(3/2), 3, 3}, {-(1/2), 3/2}, -z] == (1/(2048 (1 + z)^3)) (1832 - 25932 z - 11025 Pi^2 z^(3/2) - 107604 z^2 - 33075 Pi^2 z^(5/2) - 122500 z^3 - 33075 Pi^2 z^(7/2) - 44100 z^4 - 11025 Pi^2 z^(9/2)) + (1/(4096 (1 + z)^(13/2))) ((-4096 + 87424 z + 1022264 z^2 + 4128776 z^3 + 8300464 z^4 + 9546830 z^5 + 6402423 z^6 + 2340645 z^7 + 361830 z^8) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(4096 (1 + z)^(13/2))) ((4096 - 87424 z - 1022264 z^2 - 4128776 z^3 - 8300464 z^4 - 9546830 z^5 - 6402423 z^6 - 2340645 z^7 - 361830 z^8) Log[1 - Sqrt[z] + Sqrt[1 + z]]) - (3 (-18 + 387 z + 6160 z^2 + 14210 z^3 + 12250 z^4 + 3675 z^5) Log[Sqrt[z] + Sqrt[1 + z]])/(512 Sqrt[z] (1 + z)^(7/2)) + (1/(4096 (1 + z)^(13/2))) ((4096 - 87424 z - 1022264 z^2 - 4128776 z^3 - 8300464 z^4 - 9546830 z^5 - 6402423 z^6 - 2340645 z^7 - 361830 z^8) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) - (11025/512) z^(3/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])] - (11025/512) z^(3/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] + (11025/512) z^(3/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]

Standard Form

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MathML Form

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</mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 11025 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 25932 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1832 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 4096 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 13 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 361830 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2340645 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6402423 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> 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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]