The aim of this paper is to evaluate the weighted sums (of convergence rate ± 1 / 2 ) obtained from this series by inserting harmonic numbers into the summands.
People also ask
What is the summation of the binomial series?
How did Newton discover the binomial series?
Where does a binomial series converge?
What is the difference between binomial theorem and binomial series?
In this paper, we are going to review a particular class of binomial series (cf. [15,16,17,18]) with a free variable “y” and harmonic-like numbers.
Oct 22, 2024 · By computing definite integrals, we shall examine binomial series of convergence rate ±1/2 and weighted by harmonic-like numbers.
Nov 15, 2016 · Remark : the exact identity is ∑nr=1(−1)r−1(nr)r=∑nr=11r. One way to prove this identity is induction. Another way is as follows :.
Jan 5, 2014 · This is a consequence of binomial inversion. In general, if fn and gn are sequences such that fn=n∑k=0gk(nk). then. gn=n∑k=0(−1)n+kfk(nk).
Missing: like | Show results with:like
ABSTRACT. This paper develops the approach to the evaluation of a class of infinite series that involve special products of binomial type, generalized harmonic.
By computing definite integrals, we shall examine binomial series of convergence rate ±1/2 and weighted by harmonic-like numbers. Several closed formulae in ...
Jan 30, 2023 · Studies of series with binomials and harmonic numbers have a long history (see [14, 15]). The generating function for the central binomial ...
By computing definite integrals, we shall examine binomial series of convergence rate ±1/2 and weighted by harmonic-like numbers. Several closed formulae in ...
We derive several forms related to this sum and show how they can be useful in the probabilistic analysis of some simple variants of existing problems.
Missing: like | Show results with:like