Coefficients in Powers of the Log Series
نویسنده
چکیده
We determine the p-exponent in many of the coefficients of `(x), where `(x) is the power series for log(1+x)/x and t is any integer. In our proof, we introduce a variant of multinomial coefficients. We also characterize the power series x/ log(1 + x) by certain zero coefficients in its powers. 1. Main divisibility theorem The divisibility by primes of the coefficients in the integer powers `(x) of the power series for log(1 + x)/x, given by
منابع مشابه
Asymptotic Expansions and Positivity of Coefficients for Large Powers of Analytic Functions
We derive an asymptotic expansion as n → ∞ for a large range of coefficients of (f (z))n, where f(z) is a power series satisfying |f(z)| < f(|z|) for z ∈ C, z ∉R+. When f is a polynomial and the two smallest and the two largest exponents appearing in f are consecutive integers, we use the expansion to generalize results of Odlyzko and Richmond (1985) on log concavity of polynomials, and we prov...
متن کاملThe low energy expansion of the one-loop type II superstring amplitude
The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s log sR, where R denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the twodimensional scalar field theory propagator over the t...
متن کاملPervasive white and colored noise removing from magnetotelluric time series
Magnetotellurics is an exploration method which is based on measurement of natural electric and magnetic fields of the Earth and is increasingly used in geological applications, petroleum industry, geothermal sources detection and crust and lithosphere studies. In this work, discrete wavelet transform of magnetotelluric signals was performed. Discrete wavelet transform decomposes signals into c...
متن کاملA Priori Prediction of Tissue: Plasma Partition Coefficients (Log BP) of Drugs to Facilitate the Use of MLR and MLR-GA Methods
It is important to determine whether a candidate molecule is capable of penetrating the plasma-brain barrier indrug discovery and development. The aim of this paper is to establish a predictive model for plasma-brainbarrier penetration using simple descriptors The usefulness of the quantum chemical descriptors, calculated atthe level of the DFT and HE theories using 6-310* basis set for QSAR st...
متن کاملSolving the liner quadratic differential equations with constant coefficients using Taylor series with step size h
In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010