Geodesic
Recurrent evaluation of integrals of the type $\int^1_0x^\alpha\sin 2\pi px dx$, $\int^1_0x^\alpha\cos 2\pi px dx$ with respect to numerical stability
Applications of Mathematics, Tome 20 (1975) no. 3, pp. 206-215.

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The paper deals with recurrent processes for the evalutaion of integrals occurring in the numerical Fourier analysis. The problem of preventing a substantial influence of round-off errors accumulation is discussed and a numerically stable algorithm is developed. The theory is supplied with illustrative numerical examples.
DOI : 10.21136/AM.1975.103584
Classification : 41A55, 65D20, 65D30, 65T05 
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     author = {Chv\'ala, Franti\v{s}ek},
     title = {Recurrent evaluation of integrals of the type $\int^1_0x^\alpha\sin 2\pi px dx$, $\int^1_0x^\alpha\cos 2\pi px dx$ with respect to numerical stability},
     journal = {Applications of Mathematics},
     pages = {206--215},
     publisher = {mathdoc},
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Chvála, František. Recurrent evaluation of integrals of the type $\int^1_0x^\alpha\sin 2\pi px dx$, $\int^1_0x^\alpha\cos 2\pi px dx$ with respect to numerical stability. Applications of Mathematics, Tome 20 (1975) no. 3, pp. 206-215. doi : 10.21136/AM.1975.103584. http://geodesic.mathdoc.fr/articles/10.21136/AM.1975.103584/

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