Wahrscheinlichkeitsfunktionen diskreter Verteilungen als Lösungen der Pearsonschen Differenzengleichung für die diskreten klassischen Orthogonalpolynome.
Weighted derangements and Laguerre polynomials.
Weighted inequalities for classical and semiclassical weights.
Well-poised hypergeometric service for diophantine problems of zeta values
It is explained how the classical concept of well-poised hypergeometric series and integrals becomes crucial in studying arithmetic properties of the values of Riemann’s zeta function. By these well-poised means we obtain: (1) a permutation group for linear forms in and yielding a conditional upper bound for the irrationality measure of ; (2) a second-order Apéry-like recursion for and some low-order recursions for linear forms in odd zeta values; (3) a rich permutation group for a family...
Weyl closure of hypergeometric systems.
Widom factors for the Hilbert norm
Given a probability measure μ with non-polar compact support K, we define the n-th Widom factor W²ₙ(μ) as the ratio of the Hilbert norm of the monic n-th orthogonal polynomial and the n-th power of the logarithmic capacity of K. If μ is regular in the Stahl-Totik sense then the sequence has subexponential growth. For measures from the Szegő class on [-1,1] this sequence converges to some proper value. We calculate the corresponding limit for the measure that generates the Jacobi polynomials, analyze...
Zero distribution of sequences of classical orthogonal polynomials.
Zeros' asymptotic distribution of polynomials orthogonal with respect to varying weights.
Zeros of a certain class of Gauss hypergeometric polynomials
We prove that as , the zeros of the polynomial cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999–2001) to the case of a complex parameter and partially proves a conjecture made by the authors in an earlier work.
Zeros of smallest modulus of functions resembling exp(z).
Zonal Approximation Processes.
Zu den Orthogonalpolynomen von Althammer.
Zur Theorie der Bessel'schen Functionen
Zur Theorie der Euler'schen Integrale
Zur Theorie der Kugelfunctionen.
Zur Theorie der Kugelfunctionen.
Zur Theorie der Riemann 'schen Functionen zweiter Ordnung mit vier Verzweigungspunkten
α-Mellin Transform and One of Its Applications
MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper [5], where we have introduced the definition of the α-Mellin transform and some of its basic properties. Some examples of special cases are provided. Its operational properties as Theorem 1, Theorem 2 (Convolution theorem) and Theorem 3 (α-Mellin transform...
and some other constants.
Аналитическое продолжение по параметру функций Грина внешних краевых задач для двумерного уравнения Гельмгольца. I