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Matsaev's Theorem
Matsaev's theorem is a theorem from complex analysis, which characterizes the order and type of an entire function In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any .... The theorem was proven in 1960 by Vladimir Igorevich Matsaev. Matsaev's theorem Let f(z) with z=re^ be an entire function which is bounded from below as follows :\log(, f(z), )\geq -C\frac, where :C>0,\quad \rho>1\quad and \quad s\geq 0. Then f is of order \rho and has finite type. References Theorems in complex analysis {{improve categories, date=June 2023 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complex Analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering. As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis is particularly concerned with analytic functions of a complex variable, that is, '' holomorphic functions''. The concept can be extended to functions of several complex variables. Complex analysis is contrasted with real analysis, which dea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entire Function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any finite sums, products and compositions of these, such as the trigonometric functions sine and cosine and their hyperbolic counterparts sinh and cosh, as well as derivatives and integrals of entire functions such as the error function. If an entire function f(z) has a root at w, then f(z)/(z-w), taking the limit value at w, is an entire function. On the other hand, the natural logarithm, the reciprocal function, and the square root are all not entire functions, nor can they be continued analytically to an entire function. A transcendental entire function is an entire function that is not a polynomial. Just as meromorphic functions can be viewed as a generalization of rational fractions, entire functions can be viewed as a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vladimir Igorevich Matsaev
Vladimir (, , pre-1918 orthography: ) is a masculine given name of Slavic origin, widespread throughout all Slavic nations in different forms and spellings. The earliest record of a person with the name is Vladimir of Bulgaria (). Etymology The Old East Slavic form of the name is Володимѣръ ''Volodiměr'', while the Old Church Slavonic form is ''Vladiměr''. According to Max Vasmer, the name is composed of Slavic владь ''vladĭ'' "to rule" and ''*mēri'' "great", "famous" (related to Gothic element ''mērs'', ''-mir'', cf. Theode''mir'', Vala''mir''). The modern ( pre-1918) Russian forms Владимиръ and Владиміръ are based on the Church Slavonic one, with the replacement of мѣръ by миръ or міръ resulting from a folk etymological association with миръ "peace" or міръ "world". Max Vasmer, ''Etymological Dictionary of Russian Language'' s.v. "Владимир"starling.rinet.ru [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
