Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ac8x)

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=2

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

http://functions.wolfram.com/07.27.03.ac8x.01

Input Form

HypergeometricPFQ[{-(5/2), 2, 2}, {1/2, 7/2}, -z] == (1/(32768 z^2)) (-11520 - 2880 z + 27904 z^2 + 10800 Pi^2 z^(5/2) + 80200 z^3 + 22500 Pi^2 z^(7/2) + 44100 z^4 + 11025 Pi^2 z^(9/2)) + (1/(16384 (1 + z)^(13/2))) ((128768 - 4884768 z - 6915192 z^2 - 25811998 z^3 - 44069142 z^4 - 48970995 z^5 - 35341980 z^6 - 16051320 z^7 - 4174830 z^8 - 474495 z^9) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(16384 (1 + z)^(13/2))) ((-128768 + 4884768 z + 6915192 z^2 + 25811998 z^3 + 44069142 z^4 + 48970995 z^5 + 35341980 z^6 + 16051320 z^7 + 4174830 z^8 + 474495 z^9) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 Sqrt[1 + z] (192 - 16 z + 112 z^2 + 1010 z^3 + 735 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/(8192 z^(5/2)) + (1/(16384 (1 + z)^(13/2))) ((-128768 + 4884768 z + 6915192 z^2 + 25811998 z^3 + 44069142 z^4 + 48970995 z^5 + 35341980 z^6 + 16051320 z^7 + 4174830 z^8 + 474495 z^9) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (225 Sqrt[z] (48 + 100 z + 49 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/8192 + (225 Sqrt[z] (48 + 100 z + 49 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/8192 - (225 Sqrt[z] (48 + 100 z + 49 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ 8192

Standard Form

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MathML Form

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</cn> <ci> z </ci> </apply> <cn type='integer'> -128768 </cn> </apply> <apply> <ln /> <apply> <times /> <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> <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> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 100 </cn> <ci> z </ci> </apply> <cn type='integer'> 48 </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> </apply> </apply> </apply> <apply> <ln /> <apply> <times /> <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> <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> 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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]