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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=3, a3>=3
For fixed z and a1=1/2, a2=3, a3=3
For fixed z and a1=1/2, a2=3, a3=3, b1=-5/2
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http://functions.wolfram.com/07.27.03.aopb.01
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HypergeometricPFQ[{1/2, 3, 3}, {-(5/2), -(5/2)}, z] ==
(1/(1600 (-1 + z)^11)) (-1600 + 16448 z - 81472 z^2 - 243776 z^3 -
54067280 z^4 - 434923880 z^5 - 731637258 z^6 - 287724723 z^7 -
19037634 z^8) - (693 (1584 z^(7/2) + 41272 z^(9/2) + 172022 z^(11/2) +
178497 z^(13/2) + 45672 z^(15/2) + 1848 z^(17/2)) ArcSin[Sqrt[z]])/
(320 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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