scholarly journals Summation of certain trigonometric series with logarithmic coefficients

2021 ◽  
Author(s):  
Rufus Boyack
Keyword(s):  
Trigonometric Series ◽  
Logarithmic Coefficients

Trigonometric series with a given spectrum

2020 ◽  
Vol 2 (4) ◽  
pp. 881-906
Author(s):  
Yves Meyer
Keyword(s):  
Trigonometric Series

scholarly journals Initial logarithmic coefficients for functions starlike with respect to symmetric points

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Exact Result ◽  
Positive Real Part ◽  
Additional Benefit ◽  
Extremal Functions ◽  
Positive Real ◽  
Logarithmic Coefficients ◽  
Symmetric Points

AbstractIn this paper, we obtain the bounds of the initial logarithmic coefficients for functions in the classes $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S of functions which are starlike with respect to symmetric points and convex with respect to symmetric points, respectively. In our research, we use a different approach than the usual one in which the coeffcients of f are expressed by the corresponding coeffcients of functions with positive real part. In what follows, we express the coeffcients of f in $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S by the corresponding coeffcients of Schwarz functions. In the proofs, we apply some inequalities for these functions obtained by Prokhorov and Szynal, by Carlson and by Efraimidis. This approach offers a additional benefit. In many cases, it is easily possible to predict the exact result and to select extremal functions. It is the case for $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S .

scholarly journals On Coefficient Problems for Functions Connected with the Sine Function

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1179
Author(s):  
Katarzyna Tra̧bka-Wiȩcław
Keyword(s):  
Analytic Functions ◽  
Sine Function ◽  
Hankel Determinant ◽  
Coefficient Problems ◽  
Logarithmic Coefficients ◽  
Symmetric Points

In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates for the following: coefficients, logarithmic coefficients, some cases of the generalized Zalcman coefficient functional, and some cases of the Hankel determinant.

Integrability of Trigonometric Series

1958 ◽  
Vol 9 (2) ◽  
pp. 315
Author(s):  
J. M. Gonzalez-Fernandez
Keyword(s):  
Trigonometric Series
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