Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a7qc)

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=-5/2, a₃>=-5/2

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

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

http://functions.wolfram.com/07.27.03.a7qc.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), -(5/2)}, {5/2, 7/2}, z] == (Sqrt[1 - z] (-270 - 118305 z + 26280538 z^2 - 32559336 z^3 + 1807088 z^4))/ (33554432 z^2) + (75 (-25 Pi^2 - 1600 Pi^2 z + 14400 Pi^2 z^2 - 6400 Pi^2 z^3 + 128 Pi^2 z^4))/(16777216 (-z)^(3/2)) - (1/(33554432 (-z)^(5/2))) (15 (-18 - 4875 z - 288000 z^2 - 720000 z^3 + 1376000 z^4 - 57088 z^5) Log[Sqrt[1 - z] + Sqrt[-z]]) - (225 (-25 - 1600 z + 14400 z^2 - 6400 z^3 + 128 z^4) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/(8388608 (-z)^(3/2)) + (1/(4194304 (-z)^(3/2))) (225 (-25 - 1600 z + 14400 z^2 - 6400 z^3 + 128 z^4) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]]) + (225 (-25 - 1600 z + 14400 z^2 - 6400 z^3 + 128 z^4) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/(4194304 (-z)^(3/2)) - (225 (-25 - 1600 z + 14400 z^2 - 6400 z^3 + 128 z^4) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/(4194304 (-z)^(3/2))

Standard Form

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MathML Form

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<mrow> <mn> 4194304 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 225 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 128 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 14400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1600 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 25 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </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]