نتایج جستجو برای: complex inversion formula

تعداد نتایج: 909005  

2009
Alan D. Sokal Pierre Leroux

I show that the general implicit-function problem (or parametrized fixedpoint problem) in one complex variable has an explicit series solution given by a trivial generalization of the Lagrange inversion formula. I give versions of this formula for both analytic functions and formal power series.

Journal: :Advances in Applied Mathematics 1997

Journal: :Bulletin of the American Mathematical Society 1972

Journal: :Bulletin of the American Mathematical Society 1973

Journal: :Journal of Mathematical Physics 1978

Journal: :Journal of Pure and Applied Algebra 1992

2017
FENG QI F. QI

In the paper, the author (1) presents an explicit formula and its inversion formula for higher order derivatives of generating functions of the Bell polynomials, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds; (2) recovers an explicit formula and its inversion form...

1997
Rudolf H. Riedi Benoit B. Mandelbrot

In a previous paper MR the authors introduced the inverse measure y of a probability measure on It was argued that the respective multifractal spectra are linked by the inversion formula fy f Here the statements of MR are put in more mathematical terms and proofs are given for the inversion formula in the case of continuous measures Thereby f may stand for the Hausdor spectrum the packing spect...

Journal: :Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 2000
Ming Wen Dai Evenson

The application of the Mobius inversion formula to the specific-heat-phonon spectrum inversion problem (SPI) initially appeared promising [N.X. Chen, Phys. Rev. Lett. 64, 1193 (1990); J. Maddox, Nature (London) 344, 377 (1990)]. However, no one has previously been able to obtain the exact Debye spectrum with the correct cut-off factor and frequency dependence from the Mobius formula. The main d...

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