Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.acer)

HypergeometricPFQ

$Mathematica Notation$

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=2, a₃>=2

For fixed z and a₁=-5/2, a₂=2, a₃=3

For fixed z and a₁=-5/2, a₂=2, a₃=3, b₁=-3/2

http://functions.wolfram.com/07.27.03.acer.01

Input Form

HypergeometricPFQ[{-(5/2), 2, 3}, {-(3/2), 5/2}, z] == (3 (-320 - 1824 z - 5096 z^2 - 34300 z^3 + 11025 I Pi^2 z^(7/2) + 44100 z^4 - 11025 I Pi^2 z^(9/2)))/(8192 (-1 + z) z) + (15 Sqrt[1 - z] (-16 + 56 z + 126 z^2 + 441 z^3 - 2940 z^4 + 2205 z^5) ArcSin[Sqrt[z]])/(2048 (-1 + z)^2 z^(3/2)) - (1/(98304 (-1 + z)^9)) (Sqrt[1 - z] (-340224 + 1832064 z - 11829600 z^2 + 31597120 z^3 - 246860140 z^4 + 672057114 z^5 - 1147216549 z^6 + 1270966105 z^7 - 922348665 z^8 + 425005425 z^9 - 113193990 z^10 + 13304340 z^11) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(98304 (-1 + z)^9)) (Sqrt[1 - z] (-340224 + 1832064 z - 11829600 z^2 + 31597120 z^3 - 246860140 z^4 + 672057114 z^5 - 1147216549 z^6 + 1270966105 z^7 - 922348665 z^8 + 425005425 z^9 - 113193990 z^10 + 13304340 z^11) Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))]) - (33075 z^(5/2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))])/2048 + (1/(98304 (-1 + z)^9)) (Sqrt[1 - z] (-340224 + 1832064 z - 11829600 z^2 + 31597120 z^3 - 246860140 z^4 + 672057114 z^5 - 1147216549 z^6 + 1270966105 z^7 - 922348665 z^8 + 425005425 z^9 - 113193990 z^10 + 13304340 z^11) Log[1 + E^(I ArcSin[Sqrt[z]])]) - (33075 I z^(5/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/2048 + (33075 I z^(5/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/2048

Standard Form

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MathML Form

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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11829600 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1832064 </cn> <ci> z </ci> </apply> <cn type='integer'> -340224 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <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> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 98304 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 9 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

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,...,a_p},{b₁,...,b_q},z]