In this paper, we obtain the analytical solutions of two kinds of transcendental equations with
\nnumerous applications in college physics by means of the Lagrange inversion theorem. Afterwards we
\nrewrite them in the form of a ratio of rational polynomials by a second-order Pad\u00e9 approximant from
\na practical and instructional perspective. Our method is illustrated in a pedagogical manner for the
\nbenefit of students at the undergraduate level. The approximate formulas introduced in the paper can
\nbe applied to abundant examples in physics textbooks, such as Fraunhofer single-slit diffraction,
\nWien\u2019s displacement law, and the Schr\u00f6dinger equation with single- or double- \u03b4 potential. These
\nformulas, consequently, can reach considerable accuracies according to the numerical results;
\ntherefore, they promise to act as valuable ingredients in the standard teaching curriculum.<\/p>\n","protected":false},"excerpt":{"rendered":"
In this paper, we obtain the analytical solutions of two kinds of transcendental equations with
\nnumerous applications in college physics by means of the Lagrange inversion theorem. Afterwards we
\nrewrite them in the form of a ratio of rational polynom…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-76129","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/76129","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=76129"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/76129\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=76129"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=76129"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=76129"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}