Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2447)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃>=-5/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=-3/2

For fixed z and a₁=-7/2, a₂=-5/2, a₃=-3/2, b₁=7/2

http://functions.wolfram.com/07.27.03.2447.01

Input Form

HypergeometricPFQ[{-(7/2), -(5/2), -(3/2)}, {7/2, 7/2}, z] == (525 (Pi^2 + 80 Pi^2 z + 2400 Pi^2 z^2 - 12800 Pi^2 z^3 + 3200 Pi^2 z^4))/ (134217728 (-z)^(5/2)) + (1/(268435456 z^2)) (Sqrt[1 - z] (-38745 - 2141230 z + 200337048 z^2 - 141820496 z^3 + 2140928 z^4 + 2560 z^5)) - (1/(268435456 (-z)^(5/2))) (105 (-249 - 10560 z - 348000 z^2 - 1024000 z^3 + 832000 z^4 - 6144 z^5) Log[Sqrt[1 - z] + Sqrt[-z]]) - (1575 (1 + 80 z + 2400 z^2 - 12800 z^3 + 3200 z^4) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/(67108864 (-z)^(5/2)) + (1/(33554432 (-z)^(5/2))) (1575 (1 + 80 z + 2400 z^2 - 12800 z^3 + 3200 z^4) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]]) + (1575 (1 + 80 z + 2400 z^2 - 12800 z^3 + 3200 z^4) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/(33554432 (-z)^(5/2)) - (1575 (1 + 80 z + 2400 z^2 - 12800 z^3 + 3200 z^4) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/(33554432 (-z)^(5/2))

Standard Form

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MathML Form

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</mo> <mrow> <mn> 80 </mn> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 134217728 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2560 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2140928 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 141820496 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 200337048 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2141230 </mn> <mo> ⁢ </mo> 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</mo> <mi> z </mi> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 33554432 </mn> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 1575 </mn> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 12800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 80 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 1 </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 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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]