Generalized hypergeometric function 3F2: Specific values (formula 07.27.03.2197)

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=-5/2

http://functions.wolfram.com/07.27.03.2197.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2), 4}, {-(5/2), 7/2}, z] == (-7350 - 55370 z + 5052255 z^2 - 23027403 z^3 + 44986165 z^4 - 73634505 z^5)/ (5898240 z^2) - (49 (10 + 72 z + 1125 z^2 - 14000 z^3 + 47250 z^4 - 83160 z^5 + 48703 z^6) Log[1 - Sqrt[z]])/(786432 z^(5/2)) + (49 (10 + 72 z + 1125 z^2 - 14000 z^3 + 47250 z^4 - 83160 z^5 + 48703 z^6) Log[1 + Sqrt[z]])/(786432 z^(5/2)) + (105105 z^(7/2) PolyLog[2, -Sqrt[z]])/32768 - (105105 z^(7/2) PolyLog[2, Sqrt[z]])/32768

Standard Form

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MathML Form

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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]