Accurate sampling formula for approximating the partial derivatives of bivariate analytic functions

2020 ◽  
Author(s):  
R. M. Asharabi ◽  
J. Prestin
Keyword(s):  
Analytic Functions ◽  
Partial Derivatives ◽  
Sampling Formula ◽  
Derivatives Of

A system of functions biorthogonal with the derivatives of Chebyshev second-kind polynomials of a complex variable

2020 ◽  
Vol 17 (2) ◽  
pp. 256-277
Author(s):  
Ol'ga Veselovska ◽  
Veronika Dostoina
Keyword(s):  
Complex Plane ◽  
Complex Variable ◽  
Analytic Functions ◽  
Combinatorial Identities ◽  
Independent Interest ◽  
Closed Curves ◽  
In Series ◽  
Derivatives Of

For the derivatives of Chebyshev second-kind polynomials of a complex vafiable, a system of functions biorthogonal with them on closed curves of the complex plane is constructed. Properties of these functions and the conditions of expansion of analytic functions in series in polynomials under consideration are established. The examples of such expansions are given. In addition, we obtain some combinatorial identities of independent interest.

scholarly journals On the derivatives of bounded analytic functions

1964 ◽  
Vol 5 (3-4) ◽  
pp. 287-300 ◽  
Author(s):  
»ke Samuelsson
Keyword(s):  
Analytic Functions ◽  
Bounded Analytic Functions ◽  
Derivatives Of

scholarly journals Complex Interpolation with Derivatives of Analytic Functions

1994 ◽  
Vol 120 (2) ◽  
pp. 380-402 ◽  
Author(s):  
M. Fan ◽  
S. Kaijser
Keyword(s):  
Analytic Functions ◽  
Complex Interpolation ◽  
Derivatives Of

On Hadamard compositions of Gelfond-Leont'ev derivatives of analytic functions

2021 ◽  
pp. 67-80
Author(s):  
Myroslav Mykolayovych Sheremeta ◽  
◽  
Oksana Myroslavivna Mulyava ◽  
Keyword(s):  
Analytic Functions ◽  
Derivatives Of

Partial Derivatives of the Lambert Problem

2014 ◽  
Author(s):  
Nitin Arora ◽  
Ryan P. Russell ◽  
Nathan J. Strange
Keyword(s):  
Partial Derivatives ◽  
Lambert Problem ◽  
Derivatives Of

Perturbation theory and finite Markov chains

1968 ◽  
Vol 5 (2) ◽  
pp. 401-413 ◽  
Author(s):  
Paul J. Schweitzer
Keyword(s):  
Perturbation Theory ◽  
Markov Chain ◽  
Markov Chains ◽  
Stationary Distribution ◽  
Fundamental Matrix ◽  
Transition Probabilities ◽  
Semi Group ◽  
Partial Derivatives ◽  
Finite Markov Chains ◽  
Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

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