Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.a7pz)

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=-5/2, a₃>=-5/2

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

For fixed z and a₁=-5/2, a₂=-5/2, a₃=-5/2, b₁=1/2

http://functions.wolfram.com/07.27.03.a7pz.01

Input Form

HypergeometricPFQ[{-(5/2), -(5/2), -(5/2)}, {1/2, 5/2}, z] == (75 Sqrt[-z] (45 Pi^2 - 80 Pi^2 z + 4 Pi^2 z^2))/16384 - (Sqrt[1 - z] (-375 - 1000826 z + 8726712 z^2 - 1483216 z^3))/(1048576 z) - (15 (-25 + 3200 z - 86400 z^2 - 384000 z^3 + 51072 z^4) Log[Sqrt[1 - z] + Sqrt[-z]])/(1048576 (-z)^(3/2)) - (225 Sqrt[-z] (45 - 80 z + 4 z^2) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/8192 + (225 Sqrt[-z] (45 - 80 z + 4 z^2) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/4096 + (225 Sqrt[-z] (45 - 80 z + 4 z^2) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/ 4096 - (225 Sqrt[-z] (45 - 80 z + 4 z^2) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/4096

Standard Form

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MathML Form

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</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> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 4096 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 225 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 80 </cn> <ci> z </ci> </apply> 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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]