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Q^_

3D plot

Contour plot

Root

Re(_)>0, Q = 0

Integer root

_ = 1, Q = 0

_ = 2, Q = 0

_ = 3, Q = 0

_ = 4, Q = 0

_ = 5, Q = 0

Periodicity

periodic in _ with period (2 i π)/log(Q)

Series expansion at _ = 0

1 + _ log(Q) + 1/2 _^2 log^2(Q) + 1/6 _^3 log^3(Q) + 1/24 _^4 log^4(Q) + O(_^5)
(Taylor series)

Derivative

d/d_(Q^_) = log(Q) Q^_

Indefinite integral

integral Q^_ d_ = Q^_/log(Q) + constant

Limit

lim_(_->∞) Q^_ = 0 for log(Q)<0

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Q^_

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