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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.aquz.01
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HypergeometricPFQ[{1, 3, 7/2}, {-(7/2), -(1/2)}, z] ==
(1/(40 (-1 + z)^11)) (-40 + 200 z + 3896 z^2 - 86856 z^3 + 1999008 z^4 +
16319952 z^5 + 20054320 z^6 + 5192032 z^7 + 166048 z^8 + 99 z^9 -
54 z^10) + (9009 (128 z^(9/2) + 448 z^(11/2) + 336 z^(13/2) +
56 z^(15/2) + z^(17/2)) ArcSin[Sqrt[z]])/
(8 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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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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