𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Transcendence of Binomial and Lucas' Formal Power Series

✍ Scribed by J.-P Allouche; D Gouyou-Beauchamps; G Skordev

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
120 KB
Volume
210
Category
Article
ISSN
0021-8693

No coin nor oath required. For personal study only.

✦ Synopsis

is transcendental over ‫ޑ‬ X when t is an integer G 2. This is due to Stanley for t even, and independently to Flajolet and to Woodcock and Sharif for the general case. While Stanley and Flajolet used analytic methods and studied the asymptotics of the coefficients of this series, Woodcock and Sharif gave a purely algebraic proof. Their basic idea is to reduce this series modulo prime numbers p, and to use the p-Lucas property: if n s Ýn p i is the base p expansion of the integer n, then i 2 n i 2 n ' mod p.

📜 SIMILAR VOLUMES

Normal Subgroups in Substitution Groups
Normal Subgroups in Substitution Groups of Formal Power Series
✍ Benjamin Klopsch 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 128 KB

Let R be a commutative ring with 1, and let R = t + t 2 R͠t͡ be the group of normalized formal power series over R under substitution. In this paper we investigate the connection between the ideal structure of R and the normal subgroup structure of R . In particular, we show that, if K is a finite f

Formal power series representation for g
Formal power series representation for gauge boson stars
✍ Franz E. Schunck 📂 Article 📅 1993 🏛 John Wiley and Sons 🌐 English ⚖ 827 KB

We represent spherically symmetric, static, and non-singular solutions of the Einstein-SU(2)-Yang-Mills and the Yang-Mills-dilaton system by means of formal power series expansions. Their coefficients are algebraically expressed in terms of new recursion relations. The solutions of Bartnik and McKin

Small Sample Distribution and Power of t
Small Sample Distribution and Power of the Binomial Index of Dispersion and Log Likelihood Ratio Tests
✍ B. M. Bennett; C. Kaneshiro 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 297 KB 👁 3 views

This paper considers the exact distribution of the Xz index of dispersion and -2 log (likelihood ratio) tests for t,he hypothesis of homogeneity of c independent samples from a common binomial population. The exact significance levels and power of these tests under 'logit' alternatives are compared

Moments of power transformed time series
Moments of power transformed time series
✍ Richard W. Katz 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 94 KB 👁 1 views

A simple recursion is presented for calculating moments (e.g., mean, variance, and autocorrelation function) of a time series that has been power transformed to normality. Its derivation is elementary, relying on the moment-generating function for a bivariate normal distribution. To make clear the d