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

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=3, a₃>=3

For fixed z and a₁=-3/2, a₂=3, a₃=3

For fixed z and a₁=-3/2, a₂=3, a₃=3, b₁=1/2

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

Input Form

HypergeometricPFQ[{-(3/2), 3, 3}, {1/2, 5/2}, -z] == (-48 + 7504 z + 4050 Pi^2 z^(3/2) + 50500 z^2 + 15075 Pi^2 z^(5/2) + 44100 z^3 + 11025 Pi^2 z^(7/2))/(8192 z (1 + z)) + (1/(24576 (1 + z)^(13/2))) ((-51456 - 799656 z - 4667068 z^2 - 13137692 z^3 - 21570208 z^4 - 21669378 z^5 - 13183149 z^6 - 4476570 z^7 - 652995 z^8) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(24576 (1 + z)^(13/2))) ((51456 + 799656 z + 4667068 z^2 + 13137692 z^3 + 21570208 z^4 + 21669378 z^5 + 13183149 z^6 + 4476570 z^7 + 652995 z^8) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (3 (4 + 60 z + 2535 z^2 + 6250 z^3 + 3675 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/ (2048 z^(3/2) (1 + z)^(3/2)) + (1/(24576 (1 + z)^(13/2))) ((51456 + 799656 z + 4667068 z^2 + 13137692 z^3 + 21570208 z^4 + 21669378 z^5 + 13183149 z^6 + 4476570 z^7 + 652995 z^8) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (225 Sqrt[z] (18 + 49 z) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/2048 + (225 Sqrt[z] (18 + 49 z) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/2048 - (225 Sqrt[z] (18 + 49 z) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/2048

Standard Form

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MathML Form

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<apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 225 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 49 </cn> <ci> z </ci> </apply> <cn type='integer'> 18 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> 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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]