%0 Journal Article
%T Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder
%A Mingdong Lv
%A Hui Li
%A Huilong Ren
%A Xiaobo Chen
%J Journal of Applied Mathematics and Physics
%P 75-80
%@ 2327-4379
%D 2015
%I Scientific Research Publishing
%R 10.4236/jamp.2015.31010
%X <p class=\"MsoNormal\">
	<span lang=\"EN-US\">We consider a vertical circular cylinder on
which the vertical variation of water diffraction waves is to be represented by
a series of Laguerre functions <img src=\"Edit_4c3bc5ee-040b-401d-9c3e-ed07059a3a52.bmp\" alt=\"\" /><v:shapetype id=\"_x0000_t75\" coordsize=\"21600,21600\" o:spt=\"75\" o:preferrelative=\"t\" path=\"m@4@5l@4@11@9@11@9@5xe\" filled=\"f\" stroked=\"f\">
 <v:stroke joinstyle=\"miter\">
 <v:formulas>
  <v:f eqn=\"if lineDrawn pixelLineWidth 0\">
  <v:f eqn=\"sum @0 1 0\">
  <v:f eqn=\"sum 0 0 @1\">
  <v:f eqn=\"prod @2 1 2\">
  <v:f eqn=\"prod @3 21600 pixelWidth\">
  <v:f eqn=\"prod @3 21600 pixelHeight\">
  <v:f eqn=\"sum @0 0 1\">
  <v:f eqn=\"prod @6 1 2\">
  <v:f eqn=\"prod @7 21600 pixelWidth\">
  <v:f eqn=\"sum @8 21600 0\">
  <v:f eqn=\"prod @7 21600 pixelHeight\">
  <v:f eqn=\"sum @10 21600 0\">
 </v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
 <v:path o:extrusionok=\"f\" gradientshapeok=\"t\" o:connecttype=\"rect\">
 <o:lock v:ext=\"edit\" aspectratio=\"t\">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id=\"_x0000_i1025\" type=\"#_x0000_t75\" style=\"width:76.5pt;height:16.5pt;\" o:ole=\"\">
 <v:imagedata src=\"file:///C:\Users\fliu\AppData\Local\Temp\msohtmlclip1\01\clip_image001.wmz\" o:title=\"\">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
 <o:oleobject type=\"Embed\" progid=\"Equation.DSMT4\" shapeid=\"_x0000_i1025\" drawaspect=\"Content\" objectid=\"_1483960630\">
 </o:oleobject>
</xml><![endif]-->&nbsp;using Laguerre Polynomials <img src=\"Edit_923d36de-4055-4603-a250-13c19806236f.bmp\" alt=\"\" /><v:shape id=\"_x0000_i1026\" type=\"#_x0000_t75\" style=\"width:25.5pt;height:15pt;\" o:ole=\"\">
 <v:imagedata src=\"file:///C:\Users\fliu\AppData\Local\Temp\msohtmlclip1\01\clip_image002.wmz\" o:title=\"\">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
 <o:oleobject type=\"Embed\" progid=\"Equation.DSMT4\" shapeid=\"_x0000_i1026\" drawaspect=\"Content\" objectid=\"_1483960631\">
 </o:oleobject>
</xml><![endif]-->. The variation is assumed to be of the form <img src=\"Edit_68935579-082e-46e2-869b-90341268f9ec.bmp\" alt=\"\" /><v:shape id=\"_x0000_i1027\" type=\"#_x0000_t75\" style=\"width:45pt;height:16.5pt;\" o:ole=\"\">
 <v:imagedata src=\"file:///C:\Users\fliu\AppData\Local\Temp\msohtmlclip1\01\clip_image003.wmz\" o:title=\"\">
</v:imagedata></v:shape><!--[if gte mso 9]><xml>
 <o:oleobject type=\"Embed\" progid=\"Equation.DSMT4\" shapeid=\"_x0000_i1027\" drawaspect=\"Content\" objectid=\"_1483960632\">
%K Expansion by Laguerre Function for Wave Diffraction around an Infinite Cylinder
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53587