Identities by Generalized L−summing Method
نویسندگان
چکیده
In this paper, we introduce 3-dimensional L−summing method, which is a rearrangement of the summation P Aabc with 1 ≤ a, b, c ≤ n. Applying this method on some special arrays, we obtain some identities on the Riemann zeta function and digamma function. Also, we give a Maple program for this method to obtain identities with input various arrays and out put identities concerning some elementary functions and hypergeometric functions. Finally, we introduce a further generalization of L−summing method in higher dimension spaces.
منابع مشابه
Functional identities of degree 2 in CSL algebras
Let $mathscr{L}$ be a commutative subspace lattice generated by finite many commuting independent nests on a complex separable Hilbert space $mathbf{H}$ with ${rm dim}hspace{2pt}mathbf{H}geq 3$, ${rm Alg}mathscr{L}$ the CSL algebra associated with $mathscr{L}$ and $mathscr{M}$ be an algebra containing ${rm Alg}mathscr{L}$. This article is aimed at describing the form of additive mapppi...
متن کاملLeft Annihilator of Identities Involving Generalized Derivations in Prime Rings
Let $R$ be a prime ring with its Utumi ring of quotients $U$, $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$ and $0neq a in R$. If $R$ admits a generalized derivation $F$ such that $a(F(u^2)pm F(u)^{2})=0$ for all $u in L$, then one of the following holds: begin{enumerate} item there exists $b in U$ such that $F(x)=bx$ for all $x in R$, with $ab=0$; item $F(x)=...
متن کاملOperator Valued Series and Vector Valued Multiplier Spaces
Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous linear operators from $X$ into $Y$. If ${T_{j}}$ is a sequence in $L(X,Y)$, the (bounded) multiplier space for the series $sum T_{j}$ is defined to be [ M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}% T_{j}x_{j}text{ }converges} ] and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...
متن کاملOn Identities with Additive Mappings in Rings
begin{abstract} If $F,D:Rto R$ are additive mappings which satisfy $F(x^{n}y^{n})=x^nF(y^{n})+y^nD(x^{n})$ for all $x,yin R$. Then, $F$ is a generalized left derivation with associated Jordan left derivation $D$ on $R$. Similar type of result has been done for the other identity forcing to generalized derivation and at last an example has given in support of the theorems. end{abstract}
متن کاملContinuous Media in ( L n , g ) - Spaces . IV . Stress ( Tension ) Tensor
Basic notions of continuous media mechanics are introduced for spaces with affine connections and metrics. Stress (tension) tensors are considered, obtained by the use of the method of Lagrangians with covariant derivatives (MLCD). On the basis of the covariant Noether's identities for the energy-momentum tensors, Navier-Stokes' identities are found and generalized Navier-Cauchy as well as Navi...
متن کامل