Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Oblate spheroidal wave function
open-in-new
<h2 id="external-links">External links</h2> <ul><li>MathWorld <a href="http://mathworld.wolfram.com/SpheroidalWaveFunction.html">Spheroidal Wave functions</a></li> <li>MathWorld <a href="http://mathworld.wolfram.com/ProlateSpheroidalWaveFunction.html">Prolate Spheroidal Wave Function</a></li> <li>MathWorld <a href="http://mathworld.wolfram.com/OblateSpheroidalWaveFunction.html">Oblate Spheroidal Wave function</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>F.M. Arscott, Periodic Differential Equations, Pergamon Press (1964). <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>H.J.W. Müller, Asymptotische Entwicklungen von Sphäroidfunktionen und ihre Verwandtschaft mit Kugelfunktionen, Z. angew. Math. Mech. 44 (1964) 371-374, Über asymptotische Entwicklungen von Sphäroidfunktionen, Z. angew. Math. Mech. 45 (1965) 29-36. <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>. M. Abramowitz and I. Stegun. Handbook of Mathematical Functions pp. 751-759 (Dover, New York, 1972) <a href="http://www.math.sfu.ca/~cbm/aands/page_751.htm" target="_blank">http://www.math.sfu.ca/~cbm/aands/page_751.htm</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>C. Flammer. Spheroidal Wave Functions Stanford University Press, Stanford, CA, 1957 <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>C. Niven on the conduction of heat in ellipsoids of revolution. Philosophical transactions of the Royal Society of London, 171 p. 117 (1880) <a href="http://gallica.bnf.fr/ark:/12148/bpt6k55976x.image.f135.tableDesMatieres.langEN" target="_blank">http://gallica.bnf.fr/ark:/12148/bpt6k55976x.image.f135.tableDesMatieres.langEN</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>M. J. O. Strutt. Lamesche, Mathieusche and Verdandte Funktionen in Physik und Technik Ergebn. Math. u. Grenzeb, 1, pp. 199-323, 1932 <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>J. A. Stratton, P. M. Morse, J. L. Chu, and F. J. Corbató. Spheroidal Wave Functions Wiley, New York, 1956 <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>J. Meixner and F. W. Schafke. Mathieusche Funktionen und Sphäroidfunktionen Springer-Verlag, Berlin, 1954 <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>C. Flammer. Spheroidal Wave Functions Stanford University Press, Stanford, CA, 1957 <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>C. Flammer. Spheroidal Wave Functions Stanford University Press, Stanford, CA, 1957 <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>A. L. Van Buren, R. V. Baier, and S Hanish A Fortran computer program for calculating the oblate spheroidal radial functions of the first and second kind and their first derivatives. (1970) <a href="http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=3050792" target="_blank">http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=3050792</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>B. J. King and A. L. Van Buren A Fortran computer program for calculating the prolate and oblate spheroidal angle functions of the first kind and their first and second derivatives. (1970) <a href="http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=124589" target="_blank">http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=124589</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>R. V. Baier, A. L. Van Buren, S. Hanish, B. J. King - Spheroidal wave functions: their use and evaluation The Journal of the Acoustical Society of America, 48, pp. 102–102 (1970) <a href="https://dx.doi.org/10.1121/1.1974857" target="_blank">https://dx.doi.org/10.1121/1.1974857</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>S. Zhang and J. Jin. Computation of Special Functions, Wiley, New York, 1996 <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> <li id="fn:15"><p>W. J. Thomson Spheroidal Wave functions Archived 2010-02-16 at the Wayback Machine Computing in Science & Engineering p. 84, May–June 1999 <a href="http://www.ece.nus.edu.sg/stfpage/elelilw/Software/00764220.pdf" target="_blank">http://www.ece.nus.edu.sg/stfpage/elelilw/Software/00764220.pdf</a> <a href="#fnref:15" class="footnote-back-ref">↩</a></p></li> <li id="fn:16"><p>A. L. Van Buren and J. E. Boisvert. Accurate calculation of prolate spheroidal radial functions of the first kind and their first derivatives, Quarterly of Applied Mathematics 60, pp. 589-599, 2002 <a href="#fnref:16" class="footnote-back-ref">↩</a></p></li> <li id="fn:17"><p>A. L. Van Buren and J. E. Boisvert. Improved calculation of prolate spheroidal radial functions of the second kind and their first derivatives, Quarterly of Applied Mathematics 62, pp. 493-507, 2004 <a href="#fnref:17" class="footnote-back-ref">↩</a></p></li> <li id="fn:18"><p>C. Flammer. Spheroidal Wave Functions Stanford University Press, Stanford, CA, 1957 <a href="#fnref:18" class="footnote-back-ref">↩</a></p></li> <li id="fn:19"><p>S. Hanish, R. V. Baier, A. L. Van Buren, and B. J. King Tables of radial spheroidal wave functions, volume 4, oblate, m = 0 (1970) <a href="http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=5502362" target="_blank">http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=5502362</a> <a href="#fnref:19" class="footnote-back-ref">↩</a></p></li> <li id="fn:20"><p>S. Hanish, R. V. Baier, A. L. Van Buren, and B. J. King Tables of radial spheroidal wave functions, volume 5, oblate, m = 1 (1970) <a href="http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=124633" target="_blank">http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=124633</a> <a href="#fnref:20" class="footnote-back-ref">↩</a></p></li> <li id="fn:21"><p>S. Hanish, R. V. Baier, A. L. Van Buren, and B. J. King Tables of radial spheroidal wave functions, volume 6, oblate, m = 2 (1970) <a href="http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=124634" target="_blank">http://torpedo.nrl.navy.mil/tu/ps/doc.html?dsn=124634</a> <a href="#fnref:21" class="footnote-back-ref">↩</a></p></li> <li id="fn:22"><p>A. L. Van Buren, B. J. King, R. V. Baier, and S. Hanish. Tables of Angular Spheroidal Wave Functions, vol. 2, oblate, m = 0, Naval Research Lab. Publication, U. S. Govt. Printing Office, 1975 <a href="#fnref:22" class="footnote-back-ref">↩</a></p></li> <li id="fn:23"><p>H.J.W. Müller, Asymptotic Expansions of Oblate Spheroidal Wave Functions and their Characteristic Numbers, J. reine angew. Math. 211 (1962) 33 - 47 <a href="#fnref:23" class="footnote-back-ref">↩</a></p></li> <li id="fn:24"><p>H.J.W. Müller, Asymptotic Expansions of Prolate Speroidal Wave Functions and their Characteristic Numbers, J. reine angw. Math. 212 (1963) 26 - 48 <a href="#fnref:24" class="footnote-back-ref">↩</a></p></li> </ol>