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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=-5/2, a2>=-5/2
For fixed z and a1=-5/2, a2=1, a3>=1
For fixed z and a1=-5/2, a2=1, a3=2
For fixed z and a1=-5/2, a2=1, a3=2, b1=-3/2
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http://functions.wolfram.com/07.27.03.ab7q.01
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HypergeometricPFQ[{-(5/2), 1, 2}, {-(3/2), 7/2}, z] ==
-((I (23040 I - 10560 I z + 672 I z^2 + 1400 I z^3 + 6300 I z^4 +
1575 Pi^2 z^(9/2)))/(6144 z^2)) +
(5 Sqrt[1 - z] (-384 + 48 z + 56 z^2 + 70 z^3 + 105 z^4) ArcSin[Sqrt[z]])/
(512 z^(5/2)) + (1/(24576 (-1 + z)^8))
(Sqrt[1 - z] (-1728 + 236160 z - 4505960 z^2 - 18684730 z^3 -
1496085 z^4 - 1719382 z^5 + 2063830 z^6 - 1897350 z^7 + 1075275 z^8 -
342450 z^9 + 47220 z^10) Log[1 - E^(I ArcSin[Sqrt[z]])]) +
(1/(24576 (-1 + z)^8)) (Sqrt[1 - z] (1728 - 236160 z + 4505960 z^2 +
18684730 z^3 + 1496085 z^4 + 1719382 z^5 - 2063830 z^6 + 1897350 z^7 -
1075275 z^8 + 342450 z^9 - 47220 z^10)
Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) -
(525/512) z^(5/2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/
(1 + E^(I ArcSin[Sqrt[z]]))] - (1/(24576 (-1 + z)^8))
(Sqrt[1 - z] (-1728 + 236160 z - 4505960 z^2 - 18684730 z^3 -
1496085 z^4 - 1719382 z^5 + 2063830 z^6 - 1897350 z^7 + 1075275 z^8 -
342450 z^9 + 47220 z^10) Log[1 + E^(I ArcSin[Sqrt[z]])]) -
(525/512) I z^(5/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])] +
(525/512) I z^(5/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])]
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</apply> <apply> <times /> <cn type='integer'> 1075275 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1897350 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2063830 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1719382 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1496085 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 18684730 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4505960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 236160 </cn> <ci> z </ci> </apply> <cn type='integer'> -1728 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 1575 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6300 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1400 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 672 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10560 </cn> <imaginaryi /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 23040 </cn> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 6144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 105 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 70 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 56 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 48 </cn> <ci> z </ci> </apply> <cn type='integer'> -384 </cn> </apply> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 512 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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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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