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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, a2>=1
For fixed z and a1=1, a2=3, a3>=3
For fixed z and a1=1, a2=3, a3=7/2
For fixed z and a1=1, a2=3, a3=7/2, b1=-7/2
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http://functions.wolfram.com/07.27.03.aquy.01
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HypergeometricPFQ[{1, 3, 7/2}, {-(7/2), -(3/2)}, -z] ==
(1/(40 (1 + z)^12)) (40 + 400 z + 2832 z^2 + 59584 z^3 + 2781592 z^4 -
51329520 z^5 + 148489440 z^6 - 110984544 z^7 + 20597832 z^8 -
513654 z^9 - 75 z^10 + 90 z^11) +
(9009 (-256 z^(9/2) + 1920 z^(11/2) - 3360 z^(13/2) + 1680 z^(15/2) -
210 z^(17/2) + 3 z^(19/2)) ArcSinh[Sqrt[z]])/
(8 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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66 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 10 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 220 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <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'> 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Date Added to functions.wolfram.com (modification date)
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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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