A pair of operator summation formulas and their applications
نویسندگان
چکیده
Two types of symbolic summation formulas are reformulated using an extension of Mullin-Rota’s substitution rule in [1], and several applications involving various special formulas and identities are presented as illustrative examples.
منابع مشابه
Taylor Series for the Askey-wilson Operator and Classical Summation Formulas
Abstract. An analog of Taylor’s formula, which arises by substituting the classical derivative by a divided difference operator of Askey-Wilson type, is developed here. As an application, a generalization of the binomial theorem is obtained. Besides, this method becomes quite useful to obtain summation formulas of basic hypergeometric series. New proofs of several well-known summation formulas ...
متن کاملConvergence of the summation formulas constructed by using a symbolic operator approach
This paper deals with the convergence of the summation of power series of the form Sb a(f ;x) = ∑ a≤k≤b f(k)x k, where 0 ≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) a differentiable function defined on [a, b). Here the summation is found by using the symbolic operator approach shown in [4] . We will give a different type of the remainder of the summation formu...
متن کاملA symbolic operator approach to several summation formulas for power series II
This paper deals with the summation problem of power series of the form Sb a(f ;x) = ∑ a≤k≤b f(k)x k, where 0 ≤ a < b ≤ ∞, and {f(k)} is a given sequence of numbers with k ∈ [a, b) or f(t) is a differentiable function defined on [a, b). We present a symbolic summation operator with its various expansions, and construct several summation formulas with estimable remainders for Sb a(f ;x), by the ...
متن کامل2 5 O ct 2 00 5 Continuous and Discrete Homotopy Operators : A Theoretical Approach made Concrete ⋆
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational complex. The continuous homotopy operator automates integration by parts on the jet space. Its discrete analogue can be used in applications where summation by ...
متن کامل2 8 Ju n 20 06 Continuous and Discrete Homotopy Operators : A Theoretical Approach made Concrete ⋆
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational complex. The continuous homotopy operator automates integration by parts on the jet space. Its discrete analogue can be used in applications where summation by ...
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:
- Computers & Mathematics with Applications
دوره 58 شماره
صفحات -
تاریخ انتشار 2009