Related papers: A new Kontorovich-Lebedev-like transformation
We develop a new and further generalized form of the fractional kinetic equation involving generalized k-Bessel function. The manifold generality of the generalized k-Bessel function is discussed in terms of the solution of the fractional…
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.
We give a general surgery formula for the Casson-Walker-Lescop invariant of closed 3-manifolds, seen as the leading term of the LMO invariant, in a purely diagrammatic and combinatorial way. This provides a new viewpoint on a formula…
Generalized integral formulas involving the generalized modified k-Bessel function $J_{k,\nu }^{c,\gamma ,\lambda }\left( z\right) $ of first kind are expressed in terms generalized $k-$Wright functions. Some interesting special cases of…
In the setting of several commuting operators on a Hilbert space one defines the notions of invertibility and Fredholmness in terms of the associated Koszul complex. The index problem then consists of computing the Euler characteristic of…
This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…
Sufficient conditions are determined on the parameters such that the generalized and normalized Bessel function of the first kind and other related functions belong to subclasses of starlike and convex functions defined in the unit disk…
This paper is an exposition of heuristics related to Witten's functional integral, relating it to Vassiliev invariants and to the Kontsevich integrals that can be used to produce Vassiliev invariants of knots and links.In particular, we…
Two integral operator involving the Appell's functions, or Horn's function in the kernel are considered. Composition of such functions with generalized Bessel functions of the first kind are expressed in term of generalized Wright function…
A slight modification of the Kontorovich-Lebedev transform is an automorphism on the vector space of polynomials. The action of this $KL_{\alpha}$-transform over certain polynomial sequences will be under discussion, and a special attention…
A finite transformation method is introduced. This method is equivalent to the $Z$ transform method to a certain extent but generalizes it. By applying the presented method to the Bessel functions, it is possible to solve related ordinary…
New representations for an integral kernel of the transmutation operator and for a regular solution of the perturbed Bessel equation of the form $-u^{\prime\prime}+\left(\frac{\ell(\ell+1)}{x^{2}}+q(x)\right)u=\omega^{2}u$ are obtained. The…
A Fourier-type integral representation for Bessel's function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poisson's integral representation for the Bessel function along with a trigonometric integral…
Explicit formulae are given for the Airy and Bessel bispectral involutions, in terms of Calogero-Moser pairs. Hamiltonian structure of the motion of the poles of the operators is discussed.
In the present paper, unification of Bessel, modified Bessel, spherical Bessel and Bessel-Clifford functions via the generalized Pochhammer symbol [ Srivastava HM, Cetinkaya A, K{\i}ymaz O. A certain generalized Pochhammer symbol and its…
We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…
We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.
A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…
Recently the construction of various integral transforms for slice monogenic functions has gained a lot of attention. In line with these developments, the article at hand introduces the slice Fourier transform. In the first part, the kernel…
In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double…