Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.ac7v)

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=-3/2

http://functions.wolfram.com/07.27.03.ac7v.01

Input Form

HypergeometricPFQ[{-(5/2), 2, 2}, {-(3/2), 5/2}, -z] == (-2880 + 4704 z - 9800 z^2 + 44100 z^3 + 11025 Pi^2 z^(7/2))/(6144 z) + (1/(24576 (1 + z)^(15/2))) ((-145536 - 816320 z - 3882480 z^2 - 6044520 z^3 - 38289170 z^4 - 89699301 z^5 - 127573245 z^6 - 113089305 z^7 - 61553205 z^8 - 18905850 z^9 - 2517060 z^10) Log[1 + Sqrt[z] - Sqrt[1 + z]]) + (1/(24576 (1 + z)^(15/2))) ((145536 + 816320 z + 3882480 z^2 + 6044520 z^3 + 38289170 z^4 + 89699301 z^5 + 127573245 z^6 + 113089305 z^7 + 61553205 z^8 + 18905850 z^9 + 2517060 z^10) Log[1 - Sqrt[z] + Sqrt[1 + z]]) + (5 (48 + 56 z - 98 z^2 + 245 z^3 + 735 z^4) Log[Sqrt[z] + Sqrt[1 + z]])/ (512 z^(3/2) Sqrt[1 + z]) + (1/(24576 (1 + z)^(15/2))) ((145536 + 816320 z + 3882480 z^2 + 6044520 z^3 + 38289170 z^4 + 89699301 z^5 + 127573245 z^6 + 113089305 z^7 + 61553205 z^8 + 18905850 z^9 + 2517060 z^10) Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])]) + (3675/512) z^(5/2) Log[Sqrt[z] + Sqrt[1 + z]] Log[(-1 + Sqrt[z] + Sqrt[1 + z])/ (1 + Sqrt[z] + Sqrt[1 + z])] + (3675/512) z^(5/2) PolyLog[2, -(1/(Sqrt[z] + Sqrt[1 + z]))] - (3675/512) z^(5/2) PolyLog[2, 1/(Sqrt[z] + Sqrt[1 + z])]

Standard Form

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MathML Form

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<cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6044520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3882480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 816320 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -145536 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <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]