Lagrange inversion theorem: Difference between revisions

Revision as of 12:14, 22 March 2021

Revision as of 16:12, 28 August 2021

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:<math> W(z) e^{W(z)} = z.</math>

We may use the theorem to compute the [[Taylor series]] of <math>W(z)</math> at <math>z=0.</math> We take <math>f(w) = we^w</math> and <math>a = b = 0.</math> Recognizing that

:<math>\frac{d^n}{dx^n} e^{\alpha x} = \alpha^n e^{\alpha x},</math>