 Lebedev–Milin inequality

In mathematics, the Lebedev–Milin inequality is any of several inequalities for the coefficients of the exponential of a power series, found by Lebedev and Milin (1965) and Isaak Moiseevich Milin (1977). It was used in the proof of the Bieberbach conjecture, as it shows that the Milin conjecture implies the Robertson conjecture.
They state that if
for complex numbers β_{k} and α_{k}, and n is a positive integer, then
See also exponential formula (on exponentiation of power series).
References
 Conway, John B. (1995), Functions of One Complex Variable II, Berlin, New York: SpringerVerlag, ISBN 9780387944609, OCLC 32014394
 Korevaar, Jacob (1986), "Ludwig Bieberbach's conjecture and its proof by Louis de Branges", The American Mathematical Monthly 93 (7): 505–514, doi:10.2307/2323021, ISSN 00029890, JSTOR 2323021, MR856290
 Lebedev, N. A.; Milin, I. M. (1965), "An inequality", Vestnik Leningrad University. Mathematics 20 (19): 157–158, ISSN 0146924x, MR0186793
 Milin, I. M. (1977), Univalent functions and orthonormal systems, Providence, R.I.: American Mathematical Society, MR0369684 (Translation of the 1971 Russian edition)
Categories: Inequalities
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