منابع مشابه
Dirichlet Series
This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...
متن کاملDirichlet Series
where the an are complex numbers and s is a complex variable. Such functions are called Dirichlet series. We call a1 the constant term. A Dirichlet series will often be written as ∑ ann −s, with the index of summation understood to start at n = 1. Similarly, ∑ app −s runs over the primes, and ∑ apkp −ks runs over the prime powers excluding 1. (Not counting 1 as a prime power in that notation is...
متن کاملSome study on the growth properties of entire functions represented by vector valued Dirichlet series in the light of relative Ritt orders
For entire functions, the notions of their growth indicators such as Ritt order are classical in complex analysis. But the concepts of relative Ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. Therefore the studies of the growths of entire functions in the light of thei...
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A general initial-boundary value problem of one-dimensional transient wave propagation in a multi-layered elastic medium due to arbitrary boundary or interface excitations (either prescribed tractions or displacements) is considered. Laplace transformation technique is utilised and the Laplace transform inversion is facilitated via an unconventional method, where the expansion of complex-valued...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2012
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-012-0014-9