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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=3/2, a2>=3/2
For fixed z and a1=3/2, a2=4, a3>=4
For fixed z and a1=3/2, a2=4, a3=4
For fixed z and a1=3/2, a2=4, a3=4, b1=-5/2
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http://functions.wolfram.com/07.27.03.astq.01
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HypergeometricPFQ[{3/2, 4, 4}, {-(5/2), 1/2}, -z] ==
(1/(3840 (1 + z)^11)) (3840 + 115968 z + 2046208 z^2 + 50359040 z^3 -
480984440 z^4 + 728482975 z^5 - 254599732 z^6 + 15209068 z^7) -
(3003 (3432 z^(7/2) - 14157 z^(9/2) + 13182 z^(11/2) - 3032 z^(13/2) +
112 z^(15/2)) ArcSinh[Sqrt[z]])/(256 Sqrt[1 + z]
(1 + 11 z + 55 z^2 + 165 z^3 + 330 z^4 + 462 z^5 + 462 z^6 + 330 z^7 +
165 z^8 + 55 z^9 + 11 z^10 + z^11))
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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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