Integrals Involving Bessel Functions Research Articles

On Certain Infinite Integrals Involving Bessel Functions

Journal of Mathematics and PhysicsVolume 34, Issue 1-4 p. 179-181 Article On Certain Infinite Integrals Involving Bessel Functions† G. M. Muller, G. M. Muller Genaral Electric Company Richland, WashingtonSearch for more papers by this author G. M. Muller, G. M. Muller Genaral Electric Company Richland, WashingtonSearch for more papers by this author First published: April 1955 https://doi.org/10.1002/sapm1955341179Citations: 2 †This work was performed under contract W-31-109-Eng-52 with the Atomic Energy Commission. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume34, Issue1-4April 1955Pages 179-181 RelatedInformation

Generalisations of some Integrals Involving Bessel Functions and E-Functions

§ 1. Introductory. In § 3 a generalisation of the formula [MacRobert, Phil. Mag., Ser. 7, XXXI, p. 258]where αp+1 = ½m + ½n, αp+2 = ½m - ½n, R(m ± n) > 0, and x is real and positive, will be established. In the course of the proof Hardy's formula [Mess, of Maths., LVI, (1927), p. 190],where R(b)>0, will be required. This was originally proved by an application of Mellin's Inversion Formula. An alternative proof is given in § 2, and some related formulae are deduced.

Some Notes on Integrals Involving Bessel Functions

Journal of Mathematics and PhysicsVolume 29, Issue 1-4 p. 27-30 Article Some Notes on Integrals Involving Bessel Functions Yudell L. Luke, Yudell L. Luke Midwest Research Institute, Kansas City, MissouriSearch for more papers by this author Yudell L. Luke, Yudell L. Luke Midwest Research Institute, Kansas City, MissouriSearch for more papers by this author First published: April 1950 https://doi.org/10.1002/sapm195029127Citations: 18AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume29, Issue1-4April 1950Pages 27-30 RelatedInformation

Loop Antennas with Uniform Current

The properties of a circular loop carrying uniform current are calculated for loops of any size relative to the wavelength. The radiation resistance and the greatest directivity pass through a series of maxima and minima as the frequency is increased. At frequencies below that for which one wavelength is contained in the circumference, the directivity graph is nearly independent of frequency. As the frequency is increased, additional lobes appear, the principal lobe tending to point more nearly in the direction normal to the loop. The paper includes a note on other loops, and a mathematical appendix dealing with certain integrals involving Bessel functions.

Some Integrals Involving Bessel Functions

Journal of the London Mathematical SocietyVolume s1-13, Issue 1 p. 41-44 Notes and Papers Some Integrals Involving Bessel Functions G. N. Watson, G. N. Watson The University BirminghamSearch for more papers by this author G. N. Watson, G. N. Watson The University BirminghamSearch for more papers by this author First published: January 1938 https://doi.org/10.1112/jlms/s1-13.1.41AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volumes1-13, Issue1January 1938Pages 41-44 RelatedInformation

On series of Jacobi-polynomials and definite integrals involving Bessel functions

On series of Jacobi-polynomials and definite integrals involving Bessel functions

An infinite integral involving Bessel functions and parabolic cylinder functions

The object of this paper is to evaluate an infinite integral involving Bessel functions and parabolic cylinder functions. The following two lemmas are required:Lemma 1. provided that R(m) > 0.

Some Infinite Integrals Involving Bessel Functions

Proceedings of the London Mathematical SocietyVolume s2-40, Issue 1 p. 37-48 Papers Some Infinite Integrals Involving Bessel Functions W. N. Bailey, W. N. Bailey The University, ManchesterSearch for more papers by this author W. N. Bailey, W. N. Bailey The University, ManchesterSearch for more papers by this author First published: 1936 https://doi.org/10.1112/plms/s2-40.1.37Citations: 73AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volumes2-40, Issue11936Pages 37-48 RelatedInformation

Some series and integrals involving associated Legendre functions

1. In a recent paper I have given some definite integrals involving Legendre functions which, as a limiting case, give known results involving Bessel functions. In another paper I have shown how some integrals involving Bessel functions can be obtained from Bateman's integraland the well-known expansion

Note on Kapteyn's and Bateman's Integrals Involving Bessel Functions

Note on Kapteyn's and Bateman's Integrals Involving Bessel Functions

A Note on Some Integrals Involving Bessel Functions

The object of this note is to prove the following results, all of which hold when |a| < 1.(2) If r is any positive integer other than zero, the

Some Integrals Involving Bessel Functions

Journal of the London Mathematical SocietyVolume s1-3, Issue 1 p. 22-27 Notes and Papers Some Integrals Involving Bessel Functions G. N. Watson, G. N. WatsonSearch for more papers by this author G. N. Watson, G. N. WatsonSearch for more papers by this author First published: January 1928 https://doi.org/10.1112/jlms/s1-3.1.22AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Volumes1-3, Issue1January 1928Pages 22-27 RelatedInformation

Some Integrals Involving Bessel Functions

Journal of the London Mathematical SocietyVolume s1-2, Issue 2 p. 97-99 Notes and Papers Some Integrals Involving Bessel Functions E. C. Titchmarsh, E. C. TitchmarshSearch for more papers by this author E. C. Titchmarsh, E. C. TitchmarshSearch for more papers by this author First published: April 1927 https://doi.org/10.1112/jlms/s1-2.2.97bCitations: 5AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volumes1-2, Issue2April 1927Pages 97-99 RelatedInformation

The Asymptotic Expansions of the Spherical Harmonics

Associated Legendre Functions as Integrals involving Bessel Functions. Let,where C denotes a contour which begins at −∞ on the real axis, passes positively round the origin, and returns to −∞, amp λ=−π initially, and R(z)>0, z being finite and ≠1. [If R(z)>0 and z is finite, then R(z±)>0.] Then if I−m (λ) be expanded in ascending powers of λ, and if the resulting expression be integrated term by term, it is found that