Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 
 

 

Evaluation of the integral $ I\sb n(b)={\textstyle 2\over \pi}\int\sp\infty\sb 0\left({\sin x\over x}\right)\sp n \cos(bx)dx.$


Authors: R. G. Medhurst and J. H. Roberts
Journal: Math. Comp. 19 (1965), 113-117
MSC: Primary 65.25
DOI: https://doi.org/10.1090/S0025-5718-1965-0172446-8
MathSciNet review: 0172446
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] L. Silberstein, "The accumulation of chance effects and the Gaussian frequency distribution," Philos. Mag., v. 35, 1944, p. 395-404. MR 6, 88. MR 0010926 (6:88f)
  • [2] K. Harumi, S. Katsura & J. W. Wrench, Jr., "Values of $ (2/\pi )\int_0^\infty {{{((\sin t)/t)}^n}} dt$," Math. Comp., v. 14, 1960, p. 379. MR 22 #12737. MR 0122010 (22:12737)
  • [3] A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Tables of Integral Transforms, v. 1, McGraw-Hill, New York, 1954, p. 20. MR 15, 868.
  • [4] A. H. R. Grimsey, "On the accumulation of chance effects and the Gaussian frequency distribution," Philos. Mag., v. 36, 1945, p. 294-295. MR 7, 311. MR 0014620 (7:311a)
  • [5] L. S. Goddard, "The accumulation of chance effects and the Gaussian frequency distribution," Philos. Mag., v. 36, 1945, p. 428-433. MR 7, 311. MR 0014620 (7:311a)
  • [6] W. R. Bennett, H. E. Curtis & S. O. Rice, "Interchannel interference in FM and PM systems," Bell System Tech. J. v. 34, 1955, p. 634.
  • [7] R. Butler, "On the evaluation of $ \int_0^\infty {({{\sin }^m}t)/{t^m}} dt$ by the trapezoidal rule," Amer. Math. Monthly, v. 67, 1960, p. 566-569. MR 22 #4841. MR 0114011 (22:4841)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.25

Retrieve articles in all journals with MSC: 65.25


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1965-0172446-8
Article copyright: © Copyright 1965 American Mathematical Society

American Mathematical Society