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 ...
متن کاملComputing Fresnel integrals via modified trapezium rules
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...
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Chemical properties of cationic biosorbents, the orange peel and the lemon peel, have been studied. ATR and Raman spectra indicated that the functional groups in the peels structure responsible for dye sorption are carboxyl groups (COOH and COOM, M=Na,K,Ca,Mg) and hydroxyl groups (OH). Increasing the mass of the peels in water suspensions a decrease in dissociation of both, the –COOH and –COOM ...
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ژورنال
عنوان ژورنال: The Mathematical Intelligencer
سال: 2012
ISSN: 0343-6993,1866-7414
DOI: 10.1007/s00283-012-9304-1