Some Fundamental Solutions Which Generalize Fresnel Integrals
نویسندگان
چکیده
منابع مشابه
Computation of Fresnel Integrals
This paper describes a method for spreadsheet computations of Fresnel integrals to six significant figures, based on successive improvements of known rational approximations which are accurate to only three figures. Outside the range of validity of the improved approximations, known series expansions are used to obtain the Fresnel integrals to six figures.
متن کاملComputation of Fresnel Integrals. II
This paper describes an improved method for computing Fresnel integrals with an error of less than 1 × 10(-9). The method is based on a known approximate formula for a different integral which is due to Boersma and referenced by Abramowitz and Stegun.
متن کاملOn the Fresnel Integrals and the Convolution
The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C + (x), C − (x), S + (x), and S − (x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x r + and x r are evaluated. The Fresnel cosine integral C(x) is defined by C(x) = 2 π x 0 cos ...
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In this paper we propose methods for computing Fresnel integrals based on truncated trapezium rule approximations to integrals on the real line, these trapezium rules modified to take into account poles of the integrand near the real axis. Our starting point is a method for computation of the error function of complex argument due to Matta and Reichel (J. Math. Phys. 34 (1956), 298–307) and Hun...
متن کاملSimple Lie Algebras Which Generalize Witt Algebras
We introduce a new class of simple Lie algebras W (n, m) (see Definition 1) that generalize the Witt algebra by using " exponential " functions, and also a subalgebra W * (n, m) thereof; and we show each derivation of W * (1, 0) can be written as a sum of an inner derivation and a scalar derivation (Theorem. 2) [10]. The Lie algebra W (n, m) is Z-graded and is infinite growth [4].
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1996
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0101