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Infinite products
Kudrnáč, Vojtěch ; Rokyta, Mirko (advisor) ; Černý, Robert (referee)
This paper offers a brief insight into the basic theory of convergence of the infinite products of real or complex sequences. Then it focuses mainly on the possibilities of developing some selected functions into the form of infinite product and on the corollaries and utilizations of being familiar with these. Purpose of the paper is not to prove the existence of infinite products for functions with certain characteristics in general, but rather to derive specific formulas and prove their validity. The attention is paid to those elementary functions which are derived from the exponential function, especially the sinus function, the nonelementary functions mentioned are the gamma and the zeta function. The text should be understandable even for a person, who has never came upon infinite products before.
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Infinite products
Zavadilová, Barbora ; Seidler, Jan (advisor) ; Kaluža, Jan (referee)
We study theory of infinite products, summarize basic definitions, terms and theorems, which we apply to some elementary examples in this work. Moreover we concern with convergence of products with real factors. We also prove required and sufficient condition of convergence or absolute convergence of infinite product. The main objective of the work is derivation of sine product formula, where we also prove the theorem of exchanging limit and infinite product. These results we use for deduction cosine product formula. 1
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Infinite products
Zavadilová, Barbora ; Seidler, Jan (advisor) ; Kaluža, Jan (referee)
We study theory of infinite products, summarize basic definitions, terms and theorems, which we apply to some elementary examples in this work. Moreover we concern with convergence of products with real factors. We also prove required and sufficient condition of convergence or absolute convergence of infinite product. The main objective of the work is derivation of sine product formula, where we also prove the theorem of exchanging limit and infinite product. These results we use for deduction cosine product formula. 1
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Infinite products
Kudrnáč, Vojtěch ; Rokyta, Mirko (advisor) ; Černý, Robert (referee)
This paper offers a brief insight into the basic theory of convergence of the infinite products of real or complex sequences. Then it focuses mainly on the possibilities of developing some selected functions into the form of infinite product and on the corollaries and utilizations of being familiar with these. Purpose of the paper is not to prove the existence of infinite products for functions with certain characteristics in general, but rather to derive specific formulas and prove their validity. The attention is paid to those elementary functions which are derived from the exponential function, especially the sinus function, the nonelementary functions mentioned are the gamma and the zeta function. The text should be understandable even for a person, who has never came upon infinite products before.
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