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A New Formula for the Number of Labeled Series-Parallel Graphs
A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. A new explicit simpler formula for the...
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Faber polynomial coefficient inequalities for bi-Bazilevič functions associated with the Fibonacci-number series and the square-root functions
Two new subclasses of the class of bi-Bazilevič functions, which are related to the Fibonacci-number series and the square-root functions, are...
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Series
The concept of a series is defined and various properties of series are examined. Functional series (and, in particular, power series and related...
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Expected Number of Zeros of Random Power Series with Finitely Dependent Gaussian Coefficients
We are concerned with zeros of random power series with coefficients being a stationary, centered, complex Gaussian process. We show that the...
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A Fast Algorithm for Computing the Number of Magic Series
We present a fast algorithm for computing the number of magic series, an enumeration problem of a certain integer partition. Kinnaes showed that the...
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Sums of singular series and primes in short intervals in algebraic number fields
Gross and Smith have put forward generalizations of Hardy–Littlewood twin prime conjectures for algebraic number fields. We estimate the behaviour of...
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Eisenstein Series
In this chapter we survey the theory of Eisenstein series. Our main goal is to state Langlands’ decomposition of...
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Power Series
In this chapter, we are going to look at a special family of functions series, namely the power series. Due to the concrete form of these series, we...
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Power Series
We apply the ideas of the previous chapter to consider the convergence behavior of power series in general. We then discuss the fundamental results...
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Embedding World Series
During December 1991–January 1992, Paul Erdős and I were working on the book Problems of pgom Erdős at my home in Colorado Springs. Ron Graham called...
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Research Directions in Number Theory Women in Numbers V
This is the fifth proceedings volume published under the Women in Numbers umbrella. The WIN workshops and their proceedings volumes are part of the...
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Fourier Series
Chapter 1 covers the classical theory of Fourier series of...
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Numerical Series and Series of Functions
Let V be a normed vector space. Given a sequence (a k)k in V , the associated “series” is the sequence (s n)n defined by...
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Fourier Series
In this chapter we consider the representations of functions in the form of series in trigonometric functions. This approach will be used for solving...
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Sums and Series
In this chapter, we experience the problems of the second major area of the book, which is Sums and Series. Like in the first chapter, the reader...
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Fuzzy Time Series Analysis and Forecasting
The problem of system modeling and identification has attracted considerable attention during the past decades mostly because of a large number of...
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Some Important Series
We consider a few important series related to the Harmonic series and then Euler’s constant.
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Enumeration of Labeled Series-Parallel Tricyclic Graphs
A series-parallel graph is a graph that does not contain a complete graph with four vertices as a minor. An explicit formula for the number of...
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Exotic B-Series and S-Series: Algebraic Structures and Order Conditions for Invariant Measure Sampling
B-Series and generalizations are a powerful tool for the analysis of numerical integrators. An extension named exotic aromatic B-Series was...
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Complex Power Series
The main goal of this chapter is to show that analytic functions can be represented as infinite power series. The key to proving this theorem is the...