Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ai5s)

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=4

For fixed z and a₁=-3/2, a₂=3, a₃=4, b₁=3/2

http://functions.wolfram.com/07.27.03.ai5s.01

Input Form

HypergeometricPFQ[{-(3/2), 3, 4}, {3/2, 7/2}, -z] == (5 (192 + 352 z + 2160 Pi^2 z^(3/2) + 71400 z^2 + 25200 Pi^2 z^(5/2) + 132300 z^3 + 33075 Pi^2 z^(7/2)))/(524288 z^2) + (1/(393216 (1 + z)^(15/2))) ((-618864 - 14408528 z - 64275875 z^2 - 176965590 z^3 - 306277740 z^4 - 348028064 z^5 - 260498058 z^6 - 124131055 z^7 - 34226775 z^8 - 4165875 z^9) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(393216 (1 + z)^(15/2))) ((618864 + 14408528 z + 64275875 z^2 + 176965590 z^3 + 306277740 z^4 + 348028064 z^5 + 260498058 z^6 + 124131055 z^7 + 34226775 z^8 + 4165875 z^9) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (15 (-16 - 40 z + 2050 z^2 + 12075 z^3 + 11025 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/(131072 z^(5/2) Sqrt[1 + z]) + (1/(393216 (1 + z)^(15/2))) ((618864 + 14408528 z + 64275875 z^2 + 176965590 z^3 + 306277740 z^4 + 348028064 z^5 + 260498058 z^6 + 124131055 z^7 + 34226775 z^8 + 4165875 z^9) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])]) + (225 (48 + 560 z + 735 z^2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/(1 + Sqrt[z] + Sqrt[1 + z])])/ (131072 Sqrt[z]) + (225 (48 + 560 z + 735 z^2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))])/(131072 Sqrt[z]) - (225 (48 + 560 z + 735 z^2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])])/ (131072 Sqrt[z])

Standard Form

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MathML Form

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<ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </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> </apply> </apply> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 11025 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12075 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2050 </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'> 40 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -16 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power 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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]