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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=-1/2, a3>=-1/2
For fixed z and a1=-7/2, a2=-1/2, a3=4
For fixed z and a1=-7/2, a2=-1/2, a3=4, b1=1/2
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http://functions.wolfram.com/07.27.03.5629.01
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HypergeometricPFQ[{-(7/2), -(1/2), 4}, {1/2, 7/2}, z] ==
(-105 - 980 z + 270951 z^2 + 432369 z^3 - 203280 z^4 + 45045 z^5)/
(294912 z^2) + (35 (-1 - 9 z - 225 z^2 - 2840 z^3 + 4725 z^4 - 2079 z^5 +
429 z^6) Log[1 - Sqrt[z]])/(196608 z^(5/2)) -
(35 (-1 - 9 z - 225 z^2 - 2840 z^3 + 4725 z^4 - 2079 z^5 + 429 z^6)
Log[1 + Sqrt[z]])/(196608 z^(5/2)) - (6125 Sqrt[z] PolyLog[2, -Sqrt[z]])/
8192 + (6125 Sqrt[z] PolyLog[2, Sqrt[z]])/8192
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</mo> <msqrt> <mi> z </mi> </msqrt> <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> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mn> 8192 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 4 </cn> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 45045 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 203280 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 432369 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 270951 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 980 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -105 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 294912 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 429 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn 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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,...,ap},{b1,...,bq},z] | |
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