8 papers
The fractional Kontorovich-Lebedev transform
Semyon Yakubovich
We introduce the so-called fractional analog of the Kontorovich-Lebedev transform, modifying its kernel, which is the Macdonald function . Properties of this kernel as wel…
On the Macdonald-type function and its relation with index transforms and orthogonal polynomials
Semyon Yakubovich
We continue to investigate properties of the function which is associated with the Macdonald function in terms of the corresponding Fourier integral. In particu…
New biorthogonal sequences generated by index integrals of the weight functions
Semyon Yakubovich
We exhibit new biorthogonal sequences generated by index integrals of the squares of the modified Bessel functions and gamma functions. The composition orthogonality, involving dif…
Generalized product formulas for Whittaker's functions and a novel class of index transforms
Semyon Yakubovich
Generalized product formulas and index transforms, involving products of Whittaker's functions of different indices are established and investigated. The corresponding inversion fo…
A new index transform with the square of Whittaker's function
Semyon Yakubovich
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index tr…
Uniform upper bounds and asymptotic expansions for certain index kernels
Semyon Yakubovich
We continue to establish uniform upper bounds and asymptotic expansions for the kernels of the index transforms which were recently developed for the Kontorovich-Lebedev operator.…