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"ABSTRAKThe two-sided Lagrange-Sylvester interpolation problem is solved in the frame-work of H2 functions. The extra Hilbert-space structure allows us to give self-contained and independent arguments. "

"Polinomial Chebyshev jenis pertama dan kedua dapat direpresentasikan di dalam kuantitas kompleks yang didefinisikan oleh formula Moivre. Polinomial Chebyshev jenis pertama merupakan bagian real dari kuantitas kompleks sedangkan polinomial Chebyshev jenis kedua merupakan bagian imajiner dari kuantitas kompleks. Karena sifat keterhubungan polinomial Chebyshev di dalam kuantitas kompleks, fungsi pembangkit dari polinomial Chebyshev jenis pertama dan kedua dapat diturunkan berdasarkan bagian real dan imajiner dari fungsi pembangkit kuantitas kompleks. Dalam skripsi ini fungsi pembangkit yang akan diturunkan adalah fungsi pembangkit dari polinomial Chebyshev jenis pertama dan kedua, hasil kali dari polinomial Chebyshev jenis pertama dan kedua, serta fungsi pembangkit dari generalisasi polinomial Chebyshev jenis pertama dan kedua. Fungsi pembangkit yang akan diturunkan adalah fungsi pembangkit biasa dan fungsi pembangkit eksponensial.

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Chebyshev polynomials of the first and the second kind can be represented by a complex quantity that is defined as the Moivre formula. Chebyshev Polynomial of the first kind is related to the real part of the complex quantity whereas Chebyshev polynomial of the second kind is related to its imaginary part. In as much the existence of the relation, the generating functions of Chebyshev polynomials of the first and the second kind can be derived from the real and the imaginary part of the generating functions of the complex quantity. The generating functions derived in this mini thesis are the generating functions of Chebyshev polynomials of the first and the second kind, product of Chebyshev polynomials and the generalization of Chebyshev polynomials.The generating functions which will be derived are ordinary and exponential generating functions."

"Classical methods in analytic theory such as Mertens’ theorem and Chebyshev’s inequalities and the celebrated Prime number theorem give estimates for the distribution of prime numbers. Later on, multiplicative structure of integers leads to multiplicative arithmetical functions for which there are many important examples in number theory. Their theory involves the Dirichlet convolution product which arises with the inclusion of several summation techniques and a survey of classical results such as Hall and Tenenbaum’s theorem and the Möbius Inversion Formula. Another topic is the counting integer points close to smooth curves and its relation to the distribution of squarefree numbers, which is rarely covered in existing texts. Final chapters focus on exponential sums and algebraic number fields. A number of exercises at varying levels are also included."

"This is a foundation for arithmetic topology. A new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations."