holomorphic function

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Related to Holomorphic: Meromorphic, Analytic function, Cauchy Riemann equations

holomorphic function

[¦häl·ō¦mȯr·fik ′fəŋk·shən]
(mathematics)
References in periodicals archive ?
where P(t,X) is a polynomial in X of degree larger than 2, with holomorphic coefficients on D.
laa, An Holomorphic Study Of Smarandache Automorphic and Cross Inverse Property Loops, Proceedings of the 4th International Conference on Number Theory and Smarandache Problems, Scientia Magna, 4(2008), No.
n] be a function of a real- variable whose complex perturbation f (z)function is holomorphic in some locally convex neighborhood [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] of ([x.
theta]](N') the space of holomorphic functions on N0 with exponential growth of order [theta] and of minimal type.
For instance, the Cauchy-Riemann equations, which specify the regularity conditions for a complex-valued function to be analytic (expressible as a power series), generalize to the Lanczos equations in Minkowski spacetime, and then generalize further to the Nijenhuis tensor equations for holomorphic functions in n-dimensional space.
The major part of realization theory concerns the identification of a given holomorphic function as a transfer (characteristic) function of a system (colligation) or a linear fractional transformation of such a function.
We note that the general study of arbitrary conformal mappings between two spheres belongs historically to the realm of complex variables and holomorphic functions on the Riemann sphere (which is precisely the analytical equivalent of the complex plane augmented with a point at infinity (Kodaira 1984)).
They may be characterized in several manners: using convergence of holomorphic functions, topological properties or potential-theoretic properties, for instance.
He shows that the measure is the product of the squared modulus of a holomorphic function with the determinant of the imaginary part of the period matrix to the power of 13.
i]> S(s + c, [LAMBDA])([xi]) is holomorphic in a neighborhood of 0.
a rectangle) is conformally mapped onto another regular region, then this mapping is performed by a holomorphic function.