相关论文: Derivative formulas for Bessel, Struve and Anger-W…

The higher derivatives of the tangent and hyperbolic tangent functions are determined. Formulas for the higher derivatives of the inverse tangent and inverse hyperbolic tangent functions as polynomials are stated and proved. Using another…

In this note, by using the Hasse-Teichm\"uller derivatives, we obtain two explicit expressions for the related numbers of higher order Appell polynomials. One of them presents a determinant expression for the related numbers of higher order…

We introduce a sequence of orthogonal polynomials whose associated moments are the Rayleigh-type sums, involving the zeros of the Bessel derivative $J_\nu'$ of order $\nu$. We also discuss the fundamental properties of those polynomials…

Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…

Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are uniformly valid for unbounded real and complex values of the argument…

We introduce and study a generalized form of derivations for dendriform algebras, specifying all admissible parameter values that define these derivations. Additionally, we present a complete classification of generalized derivations for…

We extend the Faulhaber formula to the whole complex plane, obtaining an expression that fully resembles the Euler-Maclaurin summation formula, only it's exact. Thereafter, an expression for the generalized harmonic progressions valid in…

In the article, a general solution of an equation with a generalized Hilfer derivative, which has a degeneration, is constructed. Particular solutions are presented through the Kilbas-Saigo function. A representation of the solution of the…

We describe methods for computing the Kummer function $U(a,b,z)$ for small values of $z$, with special attention to small values of $b$. For these values of $b$ the connection formula that represents $U(a,b,z)$ as a linear combination of…

We prove a formula for the $n$-th derivative of the period function $T$ in a period annulus of a planar differential system. For $n = 1$, we obtain Freire, Gasull and Guillamon formula for the period's first derivative \cite{FGG}. We apply…

The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, P\'olya and Runckel.…

In the present paper, we derive the third-order differential subordination and superordination results for some analytic univalent functions defined in the unit disc. These results are associated with generalized Struve functions and are…

In this note we give a recursive formula for the derivatives of isotropic positive definite functions on the Hilbert sphere. We then use it to prove a conjecture stated by Tr\"ubner and Ziegel, which says that for a positive definite…

We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…

The n-th derivative of a tensor valued function of a tensor is defined by a finite number of coefficients each with closed form expression.

We introduce "derived Bockstein regulators" by using an idea of Nekov\'a\v{r}. We establish a general descent formalism involving derived Bockstein regulators. We give three applications of this formalism. Firstly, we show that a conjecture…

We aim to present two new generalized integral formulae involving product of generalized Struve function $\mathcal{W}_{p,b,c}\left( z\right)$, which are expressed in terms of the generalized Lauricella functions. The main results presented…

Our purpose in this present paper is to investigate generalized integration formulas containing the generalized $k$-Bessel function $W_{v,c}^{k}(z)$ to obtain the results in representation of Wright-type function. Also, we establish certain…

In this paper, we investigate recurrence relations for the Maclaurin coefficients of the products of a elementary function and the Bessel function of the first kind $\mathcal{J}(z) = h(z) J_\nu(z)$ and the modified Bessel function of the…

A class of skew derivations on complex Noetherian generalized down-up algebras $L=L(f,r,s,\gamma)$ is constructed.