More on the calculation of the integral $I_n(b) = (2/\pi ) \int _0^\infty \left (\frac {\sin x}{x}\right )^n \cos bx dx$
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- by Henry E. Fettis PDF
- Math. Comp. 21 (1967), 727-730 Request permission
References
- R. G. Medhurst and J. H. Roberts, Evaluation of the integral \[ I_n(b)={\textstyle 2\over \pi }\int ^\infty _0\left ({\sin x\over x}\right )^n \cos (bx)dx.\], Math. Comp. 19 (1965), 113β117. MR 172446, DOI 10.1090/S0025-5718-1965-0172446-8
- Rory Thompson, Evaluation of $I_{n}(b)=2\pi ^{-1}\int _{0}{}^\infty \,(\textrm {sin}x/x)^{n}\textrm {cos}(bx)\, dx$ and of similar integrals, Math. Comp. 20 (1966), 330β332. MR 192634, DOI 10.1090/S0025-5718-1966-0192634-5
- Wilhelm Magnus and Fritz Oberhettinger, Formeln und SΓ€tze fΓΌr die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948 (German). 2d ed. MR 0025629, DOI 10.1007/978-3-662-01222-2
- R. Butler, On the evaluation of $\int _{0}^{\infty }\, (\textrm {sin}^{m}t)/t^{m}dt$ by the trapezoidal rule, Amer. Math. Monthly 67 (1960), 566β569. MR 114011, DOI 10.2307/2309178
Additional Information
- © Copyright 1967 American Mathematical Society
- Journal: Math. Comp. 21 (1967), 727-730
- DOI: https://doi.org/10.1090/S0025-5718-67-99904-8