Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2259)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, a₃=4

For fixed z and a₁=-7/2, a₂=-7/2, a₃=4, b₁=3/2

http://functions.wolfram.com/07.27.03.2259.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 4}, {3/2, 7/2}, z] == (735 + 26705 z + 62717439 z^2 + 442694469 z^3 + 433560820 z^4 + 56524440 z^5)/(75497472 z^2) + (1/(50331648 z^(5/2))) (245 (1 + 36 z - 12900 z^2 - 183600 z^3 - 92025 z^4 + 237324 z^5 + 51164 z^6) Log[1 - Sqrt[z]]) - (1/(50331648 z^(5/2))) (245 (1 + 36 z - 12900 z^2 - 183600 z^3 - 92025 z^4 + 237324 z^5 + 51164 z^6) Log[1 + Sqrt[z]]) - (1225 (75 + 2800 z + 9450 z^2 + 5544 z^3 + 429 z^4) PolyLog[2, -Sqrt[z]])/ (4194304 Sqrt[z]) + (1225 (75 + 2800 z + 9450 z^2 + 5544 z^3 + 429 z^4) PolyLog[2, Sqrt[z]])/(4194304 Sqrt[z])

Standard Form

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MathML Form

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<cn type='integer'> 92025 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 183600 </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'> 12900 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 36 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 50331648 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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]