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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=1/2, a2>=1/2
For fixed z and a1=1/2, a2=1, a3>=1
For fixed z and a1=1/2, a2=1, a3=4
For fixed z and a1=1/2, a2=1, a3=4, b1=-7/2
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http://functions.wolfram.com/07.27.03.and7.01
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HypergeometricPFQ[{1/2, 1, 4}, {-(7/2), -(7/2)}, -z] ==
(1/(3920 (1 + z)^12)) (3920 + 46400 z + 251808 z^2 + 824256 z^3 +
2290608 z^4 - 57847680 z^5 + 581202880 z^6 - 1152798944 z^7 +
531151632 z^8 - 18914049 z^9 - 1168650 z^10 - 52920 z^11) -
(1287 (128 z^(9/2) - 3840 z^(11/2) + 18720 z^(13/2) - 22880 z^(15/2) +
6435 z^(17/2)) ArcSinh[Sqrt[z]])/(112 Sqrt[1 + z]
(1 + 12 z + 66 z^2 + 220 z^3 + 495 z^4 + 792 z^5 + 924 z^6 + 792 z^7 +
495 z^8 + 220 z^9 + 66 z^10 + 12 z^11 + z^12))
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<apply> <times /> <cn type='integer'> 495 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 792 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 924 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 792 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 495 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 220 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 66 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <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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