New Relations between Two Types of Bessel Function Integrals

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Previous article Next article New Relations between Two Types of Bessel Function IntegralsHenry E. FettisHenry E. Fettishttps://doi.org/10.1137/0508075PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown that, in certain special cases, the incomplete Lipschitz–Hankel integrals are related to incomplete integrals of Hankel–Nicholson type. Integrals of the form[1] M. M. Agrest and , M. S. Maksimov, Theory of incomplete cylindrical functions and their applications, Springer-Verlag, New York, 1971x+330 MR0346209 (49:10935) 0215.43401 CrossrefGoogle Scholar[2] Carl-Erik Fröberg and , Hans Wilhelmsson, Table of the function $F(a,b)=\int\sp a\sb 0J\sb 1(x)(x\sp 2+b\sp 2)\sp {-1/2}\,dx$, Kungl. Fysiogr. Sällsk. i Lund Förh., 27 (1957), 201–215 MR0091537 (19,984j) 0080.11802 Google Scholar[3] I. S. Gradshteyn and , I. M. Ryzhik, Table of integrals, series, and products, Fourth edition prepared by Ju. V. Geronimus and M. Ju. Cei˘tlin. Translated from the Russian by Scripta Technica, Inc. Translation edited by Alan Jeffrey, Academic Press, New York, 1965xlv+1086 MR0197789 (33:5952) Google Scholar[4] Yudell L. Luke, Integrals of Bessel functions, McGraw-Hill Book Co., Inc., New York, 1962xv+419 MR0141801 (25:5198) 0106.04301 Google Scholar[5] Wilhelm Magnus and , Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948viii+230 MR0025629 (10,38a) 0039.29701 CrossrefGoogle Scholar[6] E. Wai-kwok Ng, Recursive formulae for the computation of certain integrals of Bessel functions, J. Math. and Phys., 46 (1967), 223–224 MR0213626 (35:4484) 0166.07502 CrossrefISIGoogle Scholar[7] L. Schwarz, Untersuchung einiger mit den Zylinderfunktionen nullter Ordnung verwandter Funktionen, Luftfahrtforschung, 20 (1944), 341–372 MR0010017 (5,238d) 0063.06832 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Evaluation of integrals and the mellin transformJournal of Soviet Mathematics, Vol. 54, No. 6 | 1 May 1991 Cross Ref Volume 8, Issue 6| 1977SIAM Journal on Mathematical Analysis923-1091 History Submitted:09 April 1976Published online:03 August 2006 InformationCopyright © 1977 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0508075Article page range:pp. 978-982ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics