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Recurrent evaluation of integrals of the type \(\int^1_0x^\alpha\sin 2\pi pxdx\), \(\int^1_0x^\alpha\cos 2\pi pxdx\) with respect to numerical stability. (English) Zbl 0307.65033

MSC:

65D30 Numerical integration
65D20 Computation of special functions and constants, construction of tables
41A55 Approximate quadratures
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References:

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[2] Крылов В. И.: Приближенное вычисление интегралов. Hauka, Москва 1967, гл. 14. · Zbl 1103.35360
[3] Babušková R.: Über numerische Stabilität einiger Rekursionsformeln. Apl. mat. 9 (1964), 186-193. · Zbl 0123.11104
[4] Babuška I., Práger M., Vitásek E.: Numerical processes in differential equations. Wiley, London-New York-Sydney 1966, chap. 2. · Zbl 0156.16003
[5] Fleckner O. L.: A method for the computation of the Fresnel integrals and related functions. Math. Comp. 22 (1968), 635-640. · Zbl 0159.45201
[6] Bulirsch R., Stoer J.: Numerical treatment of ordinary differential equations by extrapolation methods. Numer. Math. 8 (1966), 1 - 13. · Zbl 0135.37901
[7] Chvála F.: Evaluation of integrals by means of recurrence formulae. Report ÚVT ČVUT 2/73
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