<br><p><b>Identifier</b>: elementarytreati00byerrich (<a class="external text" href="https://commons.wikimedia.org/w/index.php?title=Special%3ASearch&amp;profile=default&amp;fulltext=Search&amp;search=insource%3A%2Felementarytreati00byerrich%2F">find matches</a>)<br><b>Title</b>: <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/bookidelementarytreati00byerrich">An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics, with applications to problems in mathematical physics</a><br><b>Year</b>: <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/bookyear1893">1893</a> (<a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/bookdecade1890">1890s</a>)<br><b>Authors</b>:  <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/bookauthorByerly__William_Elwood__1849_1935">Byerly, William Elwood, 1849-1935</a><br><b>Subjects</b>:  <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/booksubjectFourier_series">Fourier series</a> <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/booksubjectHarmonic_analysis">Harmonic analysis</a><br><b>Publisher</b>:  <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/bookpublisherBoston__Ginn___Company">Boston, Ginn &amp; Company</a><br><b>Contributing Library</b>:  <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/bookcontributorUniversity_of_California_Libraries">University of California Libraries</a><br><b>Digitizing Sponsor</b>:  <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/booksponsorMSN">MSN</a><br><br><b>View Book Page</b>: <a rel="nofollow" class="external text" href="https://archive.org/stream/elementarytreati00byerrich/elementarytreati00byerrich#page/n201/mode/1up">Book Viewer</a><br><b>About This Book</b>: <a rel="nofollow" class="external text" href="https://archive.org/details/elementarytreati00byerrich">Catalog Entry</a><br><b>View All Images</b>: <a rel="nofollow" class="external text" href="https://www.flickr.com/photos/internetarchivebookimages/tags/bookidelementarytreati00byerrich">All Images From Book</a><br>
Click here to <a rel="nofollow" class="external text" href="https://archive.org/stream/elementarytreati00byerrich/elementarytreati00byerrich#page/n201/mode/1up"><b>view book online</b></a> to see this illustration in context in a browseable online version of this book.<br><br><b>Text Appearing Before Image:</b><br><i>l Harmonic Series withdevelopment in Fouriers Series we give on page 185 a cut representing thefirst seven Surface Zonal Harmonics Pi(cos 6), P2(cos 6), • • •P7(cos 0), whichare of course somewhat complicated Trigonometric curves resembling roughlycos^, cos2^, ••-cos 7^; and on page 186, the first four successive approxi-mations to the Zonal Harmonic Series 1 + ^ P,(cos 6)-l.l P3(cos ^) + j;- II JsCcos 6) (I) (v. (1) Art. 93), and I (Po(cos 0) - 3 Q Vi(cos 0) - 7 (^)^3(cos 0) -iK2sy^^(^°^^)--)M (v. Ex. 3 Art. 97). 7j- 7j- (i) is equal to 1 from ^ = 0 to 0 = jj, and to 0 from 6 = -^ to 0 = 7r; and (ii) is equal to 6 from 6 = 0 to 6---^=7r. The figures on page 186 are constructed on precisely the same principle asthose on pages 63 and 64, with which they should be carefully compared. 98. By applying Gausss Theorem (B. 0. Peirce, Newt. Pot. Func. § 31) orthe special Form of Greens Theorem. ( ( f^^ ^dx dij dz = Cd,^ Vds = — 4.7rCC Cpdx dy dz, Chap. V.) ZONAL HARMONIC CURVES,</i><br><b>Text Appearing After Image:</b><br><i>186 ZONAL HARMONICS. (Art. 9/ -) ^ ^^ ^ ~--,~ \ ^\ ,— \-. » / &gt; &lt;: 0 / ■^^ V .^. It __,. v_ V</i><br><br><b>Note About Images</b><br></p>
<i>Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original work.</i>
Byerly, William Elwood, 1849-1935
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<ul><li>Source book page: <a rel="nofollow" class="external free" href="https://archive.org/stream/elementarytreati00byerrich/elementarytreati00byerrich#page/n201/mode/1up">https://archive.org/stream/elementarytreati00byerrich/elementarytreati00byerrich#page/n201/mode/1up</a></li></ul>