Though the definitions coincide word for word, complex differentiability has a quite different meaning than differentiability of functions of one real variable familiar to the reader from the first-year analysis course. The differences are, if you like, the subject matter of the entire book, but ...
When a polinomial is constructed using the KroghInterpolator() function from scipy.interpolate with some of the entries being complex, the resulting polinomial is complex. This works fine. However, attempting to retrieve the derivatives of this complex polinomial using the derivatives() function resul...
Complex derivatives are descriptions of the rates of change of complex functions, which operate in value fields that include imaginary numbers. They tell mathematicians about the behavior of functions that are difficult to visualize. The derivative of a complex functionfat x0, if it exists, is giv...
[14] LAHIRI, I.: Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206. 10.1017/S0027763000027215Search in Google Scholar [15] LAHIRI, I.: Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), 241–253...
作者: K Leśniewski 摘要: We investigate the relationship between the existence of directional derivatives for cone-convex functions with values in a Banach space Y and isomorphisms between Y and c0. 关键词: Mathematics - Optimization and Control DOI: 10.12775/TMNA.2019.017 年份: 2017 收藏...
composite function is the product of the derivative of the outer function evaluated at the inner function and the derivative of the inner function. This rule simplifies the differentiation of complex nested functions, playing a crucial role in advanced mathematical, scientific, and engineering ...
aThese are functions that possess complex derivatives in lots of places, a fact which endows these functions with some of the most beautiful properties mathematics has to offer. We’ll explore these properties! 这些是在许多拥有复杂衍生物地方的作用,资助这些作用与某些最美好的物产数学必须提供的事实。
Inner functions are an important and popular object of study in the field of complex function theory. We look at meromorphic inner functions with a given spectrum and provide sufficient conditions for them to have uniformly bounded derivative on the real line. This question was first studied by ...
Meromorphic functions sharing four small functions It is well known that if two nonconstant meromorphic functions f and g on the complex plane ℂ have the same inverse images counted with multiplicities f... Tran,Van,Tan - 《Abhandlungen Aus Dem Mathematischen Seminar Der Universität Hamburg》...
The Heun functions satisfy linear ordinary differential equations of second order with certain singularities in the complex plane. The first order derivatives of the Heun functions satisfy linear second order differential equations with one more singularity. In this paper we compare these equations with ...