Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Some integrals relating to the $I_{e}$-function
HTML articles powered by AMS MathViewer

by Shigehiko Okui PDF
Math. Comp. 41 (1983), 613-622 Request permission

Abstract:

Various integrals relating to the ${I_e}$-function \[ {I_e}(k,z) = \int _0^z {{e^{ - x}}{I_0}(kx)\;dx,} \] which finds a wide variety of applications in the fields of statistical communication theory and noise analysis, are evaluated in closed form.
References
  • S. O. Rice, Statistical properties of a sine wave plus random noise, Bell System Tech. J. 27 (1948), 109–157. MR 23483, DOI 10.1002/j.1538-7305.1948.tb01334.x
  • Minoru Nakagami, On the intensity distribution \[ {2R\over \surd (\alpha \beta )}\exp \left [-{R^2\over 2} \left ({1\over \alpha }+{1\over \beta }\right )\right ]I_0 \left ({R^2\over 2}\left [{1\over \beta }-{1\over \alpha }\right ]\right )\] and its application to signal statistics, J. Res. Nat. Bur. Standards Sect. D 68D (1964), 995–1003. MR 0165836
  • W. R. Bennett & J. R. Davey, Data Transmission, McGraw-Hill, New York, 1965. S. Okui, N. Morinaga & T. Namekawa, "Statistical properties of maximal ratio combining diversity in correlated m-fading environments," Trans. IECE Japan, v. 62-B, 1979, pp. 283-290. F. Adachi, "Selection and scanning diversity effects in a digital FM land mobile radio with limiter discriminator detection," Trans. IECE Japan, v. 64-E, 1981, pp. 398-405. R. F. Pawula, S. O. Rice & J. H. Roberts, "Distribution of the phase angle between two vectors perturbed by Gaussian noise," IEEE Trans. Comm., v. COM-30, 1982, pp. 1828-1841. A. Erdelyi et al. (ed.), Higher Transcendental Functions, Vols. 1-3, McGraw-Hill, New York, 1955. A. Erdelyi et al. (ed.), Tables of Integral Transforms, Vols. 1 and 2, McGraw-Hill, New York, 1955. I. S. Gradshteyn & I. M. Ryzhik, Tables of Integrals, Series, and Products, Corrected and enlarged edition, Academic Press, New York, 1980.
  • Yudell L. Luke, Integrals of Bessel functions, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR 0141801
  • F. A. J. Ford, Some infinite integrals involving products of Bessel functions, J. London Math. Soc. 41 (1966), 728–730. MR 200493, DOI 10.1112/jlms/s1-41.1.728
  • William C. Lindsey, Infinite integrals containing Bessel function products, J. Soc. Indust. Appl. Math. 12 (1964), 458–464. MR 167659, DOI 10.1137/0112038
  • M. M. Agrest and M. S. Maksimov, Theory of incomplete cylindrical functions and their applications, Die Grundlehren der mathematischen Wissenschaften, Band 160, Springer-Verlag, New York-Heidelberg, 1971. Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee. MR 0346209, DOI 10.1007/978-3-642-65021-5
  • Keith R. Lassey, On the computation of certain integrals containing the modified Bessel function $I_{0}(\xi )$, Math. Comp. 39 (1982), no. 160, 625–637. MR 669654, DOI 10.1090/S0025-5718-1982-0669654-6
  • Fritz Oberhettinger and Larry Badii, Tables of Laplace transforms, Springer-Verlag, New York-Heidelberg, 1973. MR 0352889, DOI 10.1007/978-3-642-65645-3
  • A. H. Nuttall, Some Integrals Involving the Q-Function, NUSC Tech. Report 4297, 1972.
  • Shigehiko Okui, Complete elliptic integrals resulting from infinite integrals of Bessel functions, J. Res. Nat. Bur. Standards Sect. B 78B (1974), 113–135. MR 352566, DOI 10.6028/jres.078B.018
  • Shigehiko Okui, Complete elliptic integrals resulting from infinite integrals of Bessel functions. II, J. Res. Nat. Bur. Standards Sect. B 79B (1975), no. 3-4, 137–170. MR 419888, DOI 10.6028/jres.079B.014
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC: 33A40, 94A05
  • Retrieve articles in all journals with MSC: 33A40, 94A05
Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 41 (1983), 613-622
  • MSC: Primary 33A40; Secondary 94A05
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0717707-7
  • MathSciNet review: 717707