Evaluations of Binomial Series

نویسندگان

  • Jonathan M. Borwein
  • Roland Girgensohn
چکیده

We give closed forms, recursion formulas and experimental results for the series ∑ nk/ ( 2n n ) and ∑ 2−nnk/ ( 3n n ) with k ∈ Z. Mathematics Subject Classification (2000). Primary 05A10, 11B65; Secondary 11Y16, 11Y65.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

On Bivariate Generalized Exponential-Power Series Class of Distributions

In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains the bivariate generalized exponential-Poisson, bivariate generalized exponential-logarithmic, bivariate generalized exponential-binomial and bivariate generalized exponential-negative binomial distributions as specia...

متن کامل

Heterogeneity in the usability evaluation process

Current prediction models for usability evaluations are based on stochastic distributions derived from series of Bernoulli processes. The underlying assumption of these models is a homogeneous detection probability despite of it being intuitively unrealistic. This paper contributes a simple statistical test for existence of heterogeneity in the process. The compound beta-binomial model is propo...

متن کامل

Empirically Determined Apéry-Like Formulae for ζ(4n+3)

Research supported by NSERC, the Natural Sciences and Engineering Research Council of Canada. Some rapidly convergent formulae for special values of the Riemann zeta function are given. We obtain a generating function formula for (4n+3) that generalizes Apéry’s series for (3), and appears to give the best possible series relations of this type, at least for n< 12. The formula reduces to a finit...

متن کامل

M ay 2 00 5 Empirically Determined Apéry - Like Formulae for ζ ( 4 n + 3 )

Abstract. Some rapidly convergent formulae for special values of the Riemann Zeta function are given. We obtain a generating function formula for ζ(4n+3) which generalizes Apéry’s series for ζ(3), and appears to give the best possible series relations of this type, at least for n < 12. The formula reduces to a finite but apparently non-trivial combinatorial identity. The identity is equivalent ...

متن کامل

Fitting of Count Time Series Models on the Number of Patients Referred to Addiction Treatment Centers in Semnan County

Abstract. Count data over time are observed in many application areas. Many researchers use time series patterns to analyze this data. In this paper, the poisson count time series linear models and negative binomials on this type of data with the explanatory variables are studied. The Likelihood analysis and the evaluation of count time series model based on generalized linear models are pres...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004