Limit formulas for q-exponential functions
β Scribed by Don Rawlings
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 240 KB
- Volume
- 126
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
q-Analogues are given for the limit formulas e'=lim,+,(l -t/n)-' and e'=lim,,,
(1 + t/n)'. The q-extension of the first identity is applied in proving that the probability of a q-random mapping having no fixed points approaches the reciprocal of a q-analogue of the real number e.
π SIMILAR VOLUMES
We obtain, for entire functions of exponential type, a complementary result and a generalization of a quadrature formula with nodes at the zeros of Bessel functions. Our formula contains a sequence of rational fractions whose properties are studied.
In this paper, we study formal power series with exponents in a category. For example, the generating function of a category E E with finite hom sets is defined by Ε½ . X < Ε½ .< E E t s Γt r Aut X , where the summation is taken over all isomorphism classes of objects of E E. We can use such power se