منابع مشابه
Chapter 1 Stirling ’ s Formula
How do the two most important fundamental constants of mathematics, e and π, find their way into an asymptotic formula for the product of integers? We give two very different arguments (one will not show the full formula) that, between them, illustrate a good number of basic asymptotic methods. The formal language of Asymptopia, such as o(n) and O(n), is deferred to Chapter 2. Two further argum...
متن کاملA substantial improvement of the Stirling formula
We introduce the approximation formula n! p 2 n n e + 1 12en n for the factorial function. Finally, some numerical computations are made to prove the superiority over other well-known formulas. MSC: 40A25; 41A60;
متن کاملThe Lagrange Interpolation Formula and Stirling Numbers
and the formulas may be used to extend the definition of Si(w, ¿) and S2(n, k) for arbitrary real n. In a previous paper [2] the writer has proved several apparently new formulas relating the two kinds of Stirling numbers to each other. Carlitz [l] has generalized these results in part as follows. Instead of considering the polynomial B['\ let fk(z) denote an arbitrary polynomial in z of degree...
متن کاملa haar wavelets approach to stirling's formula
this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.
متن کاملA generalized recurrence formula for Stirling numbers and related sequences
In this note, we provide a combinatorial proof of a generalized recurrence formula satisfied by the Stirling numbers of the second kind. We obtain two extensions of this formula, one in terms of r-Whitney numbers and another in terms of q-Stirling numbers of Carlitz. Modifying our proof yields analogous formulas satisfied by the r-Stirling numbers of the first kind and by the r-Lah numbers.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ??????????? ???????
سال: 2021
ISSN: ['2617-5525', '2617-5533']
DOI: https://doi.org/10.22405/2226-8383-2021-22-5-350-353