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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.astv.01
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HypergeometricPFQ[{3/2, 4, 4}, {-(5/2), 5/2}, z] ==
(384 - 4672 z + 29712 z^2 - 149768 z^3 + 1137817 z^4 + 2430228 z^5 +
385124 z^6)/(1280 (-1 + z)^9 z) +
(3 (-128 + 1216 z - 5168 z^2 + 12920 z^3 - 20995 z^4 + 667238 z^5 +
573144 z^6 + 48048 z^7) ArcSin[Sqrt[z]])/
(1280 Sqrt[1 - z] (-z^(3/2) + 9 z^(5/2) - 36 z^(7/2) + 84 z^(9/2) -
126 z^(11/2) + 126 z^(13/2) - 84 z^(15/2) + 36 z^(17/2) - 9 z^(19/2) +
z^(21/2)))
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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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