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

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=1, a₃>=1

For fixed z and a₁=-5/2, a₂=1, a₃=3

For fixed z and a₁=-5/2, a₂=1, a₃=3, b₁=-3/2

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

Input Form

HypergeometricPFQ[{-(5/2), 1, 3}, {-(3/2), 5/2}, -z] == (3 (320 + 672 z - 1400 z^2 + 6300 z^3 + 1575 Pi^2 z^(7/2)))/(4096 z) + (1/(49152 (1 + z)^(15/2))) ((11328 + 152800 z + 1035720 z^2 - 1677980 z^3 - 3809840 z^4 - 8712117 z^5 - 11826725 z^6 - 10083465 z^7 - 5306175 z^8 - 1581750 z^9 - 205020 z^10) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(49152 (1 + z)^(15/2))) ((-11328 - 152800 z - 1035720 z^2 + 1677980 z^3 + 3809840 z^4 + 8712117 z^5 + 11826725 z^6 + 10083465 z^7 + 5306175 z^8 + 1581750 z^9 + 205020 z^10) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 (-16 + 24 z - 42 z^2 + 105 z^3 + 315 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/ (1024 z^(3/2) Sqrt[1 + z]) + (1/(49152 (1 + z)^(15/2))) ((-11328 - 152800 z - 1035720 z^2 + 1677980 z^3 + 3809840 z^4 + 8712117 z^5 + 11826725 z^6 + 10083465 z^7 + 5306175 z^8 + 1581750 z^9 + 205020 z^10) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) + (4725 z^(5/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/1024 + (4725 z^(5/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/1024 - (4725 z^(5/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/1024

Standard Form

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MathML Form

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</mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8712117 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3809840 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1677980 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1035720 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 152800 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 11328 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> + </mo> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> 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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]