<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1870-3542</journal-id>
<journal-title><![CDATA[Revista mexicana de física E]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. mex. fís. E]]></abbrev-journal-title>
<issn>1870-3542</issn>
<publisher>
<publisher-name><![CDATA[Sociedad Mexicana de Física]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1870-35422016000100040</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Two-dimensional harmonic and Green&#8217;s functions on a spherical surface]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Esparza-López]]></surname>
<given-names><![CDATA[Ch.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ley-Koo]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Rendón]]></surname>
<given-names><![CDATA[P.L.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional Autónoma de México Instituto de Física ]]></institution>
<addr-line><![CDATA[México ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional Autónoma de México Centro de Ciencias Aplicadas y Desarrollo Tecnológico ]]></institution>
<addr-line><![CDATA[México ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2016</year>
</pub-date>
<volume>62</volume>
<numero>1</numero>
<fpage>40</fpage>
<lpage>43</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1870-35422016000100040&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1870-35422016000100040&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1870-35422016000100040&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[The solutions of the Laplace-Beltrami equation on a spherical surface are constructed by the method of separation of variables, as the products of the Fourier basis functions of the azimuthal angle and the integer powers of tangent or cotangent functions of half the polar angle. The Legendre operator acting on the latter functions yields zero. The construction of the Green&#8217;s function as the solution of the corresponding Poisson-Beltrami equation with a unit point source on the spherical surface is also constructed using the two-dimensional spherical harmonic basis.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Laplace-Beltrami and Poisson-Beltrami operators and equations]]></kwd>
<kwd lng="en"><![CDATA[two-dimensional spherical harmonics]]></kwd>
<kwd lng="en"><![CDATA[Green's functions]]></kwd>
<kwd lng="en"><![CDATA[separability and integrability]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bogomolov]]></surname>
<given-names><![CDATA[V. A.]]></given-names>
</name>
</person-group>
<source><![CDATA[Izv. Atmos. Ocean. Phys.]]></source>
<year>1979</year>
<volume>15</volume>
<page-range>18-22</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kimura]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Okamoto]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<source><![CDATA[J. Phys. Soc. Jpn.]]></source>
<year>1987</year>
<volume>56</volume>
<page-range>4203-6</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Crowdy]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Cloke]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Phys. Fluids]]></source>
<year>2003</year>
<volume>15</volume>
<page-range>22-34</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rendón]]></surname>
<given-names><![CDATA[P. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Ley-Koo]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Rev. Mex. Fis.]]></source>
<year>2015</year>
<volume>61</volume>
<page-range>196-206</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Arfken]]></surname>
<given-names><![CDATA[G. B.]]></given-names>
</name>
<name>
<surname><![CDATA[Weber]]></surname>
<given-names><![CDATA[H. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Harris]]></surname>
<given-names><![CDATA[F. E.]]></given-names>
</name>
</person-group>
<source><![CDATA[Mathematical Methods for Physicists: A Comprehensive Guide]]></source>
<year>2012</year>
<edition>7</edition>
<publisher-loc><![CDATA[Oxford, Great Britain ]]></publisher-loc>
<publisher-name><![CDATA[Academic Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Needham]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
</person-group>
<source><![CDATA[Visual Complex Analysis]]></source>
<year>1997</year>
<publisher-loc><![CDATA[Oxford, Great Britain ]]></publisher-loc>
<publisher-name><![CDATA[Oxford University Press]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
