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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=5/2, a2>=5/2
For fixed z and a1=5/2, a2=4, a3>=4
For fixed z and a1=5/2, a2=4, a3=4
For fixed z and a1=5/2, a2=4, a3=4, b1=-5/2
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http://functions.wolfram.com/07.27.03.auo3.01
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HypergeometricPFQ[{5/2, 4, 4}, {-(5/2), -(1/2)}, -z] ==
(1/(768 (1 + z)^13)) (768 - 14592 z - 1693184 z^2 - 123553280 z^3 +
3484987104 z^4 - 16796865488 z^5 + 24464681098 z^6 - 11895545493 z^7 +
1747587828 z^8 - 50335908 z^9) +
(15015 (13728 z^(7/2) - 157872 z^(9/2) + 469950 z^(11/2) -
473995 z^(13/2) + 166554 z^(15/2) - 17640 z^(17/2) + 336 z^(19/2))
ArcSinh[Sqrt[z]])/(256 Sqrt[1 + z] (1 + 13 z + 78 z^2 + 286 z^3 +
715 z^4 + 1287 z^5 + 1716 z^6 + 1716 z^7 + 1287 z^8 + 715 z^9 +
286 z^10 + 78 z^11 + 13 z^12 + z^13))
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type='integer'> 1693184 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14592 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 768 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 15015 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 336 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 17640 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 166554 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 473995 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 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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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