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Analytic continuation of natural logarithm (imaginary part) Analytic continuation is a technique to extend the domain of a given analytic function.Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which it is initially defined becomes divergent.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
The stability function of an explicit Runge–Kutta method is a polynomial, so explicit Runge–Kutta methods can never be A-stable. [32] If the method has order p, then the stability function satisfies () = + (+) as . Thus, it is of interest to study quotients of polynomials of given degrees that approximate the exponential function the best.
In algebraic geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V.In classical algebraic geometry they are ratios of polynomials; in complex geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions.
Combining two equal glide plane operations gives a pure translation with a translation vector that is twice that of the glide reflection, so the even powers of the glide reflection form a translation group. In the case of glide-reflection symmetry, the symmetry group of an object contains a glide reflection and the group generated by it. For ...
Steiner used the power of a point for proofs of several statements on circles, for example: Determination of a circle, that intersects four circles by the same angle. [2] Solving the Problem of Apollonius; Construction of the Malfatti circles: [3] For a given triangle determine three circles, which touch each other and two sides of the triangle ...
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