<?xml version="1.0" encoding="UTF-8"?>
<Worksheet><Version major="6" minor="0"/><View-Properties><Zoom percentage="100"/></View-Properties><Styles><Layout alignment="left" linebreak="space" name="Warning"/><Layout alignment="left" linespacing="0.5" name="_pstyle12"/><Layout name="Normal"/><Layout alignment="centred" linespacing="0.5" name="Maple Output"/><Font background="[0,0,0]" family="Monospaced" foreground="[0,0,255]" name="Warning" readonly="true" size="10"/><Font background="[0,0,0]" family="Times New Roman" foreground="[0,0,255]" name="2D Output" underline="false"/><Font background="[0,0,0]" bold="true" executable="true" family="Monospaced" foreground="[255,0,0]" name="Maple Input"/></Styles><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">restart;</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Phi := (i,j,z) -&gt; piecewise(
z&lt;=0,int(phi(i,x)*phi(j,x-z),x=0..z+1), 
z&gt;0, int(phi(i,x)*phi(j,x-z),x=z..1));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRQaGlHNiJmKjYlSSJpR0YlSSJqR0YlSSJ6R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSpwaWVjZXdpc2VHSSpwcm90ZWN0ZWRHRjA2JjE5JiIiIS1JJGludEdGJTYkKiYtSSRwaGlHRiU2JDkkSSJ4R0YlIiIiLUY6NiQ5JSwmRj1GPkYzISIiRj4vRj07RjQsJkYzRj5GPkY+MkY0RjMtRjY2JEY4L0Y9O0YzRj5GJUYlRiU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">phi := (i,x) -&gt; piecewise(x&lt;0,0,x&lt;1,sqrt(2*i+1) * P(i,2*x-1),x&gt;1,0);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRwaGlHNiJmKjYkSSJpR0YlSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSpwaWVjZXdpc2VHSSpwcm90ZWN0ZWRHRi82KDI5JSIiIUYzMkYyIiIiKiYtSSVzcXJ0R0YlNiMsJjkkIiIjRjVGNUY1LUkiUEdGJTYkRjssJkYyRjwhIiJGNUY1MkY1RjJGM0YlRiVGJQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">phi := (i,x) -&gt; sqrt(2*i+1) * P(i,2*x-1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSRwaGlHNiJmKjYkSSJpR0YlSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUqJi1JJXNxcnRHRiU2IywmOSQiIiMiIiJGNEY0LUkiUEdGJTYkRjIsJjklRjMhIiJGNEY0RiVGJUYl</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">with(orthopoly):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cplus := (i,j,p) -&gt; simplify(int(int(phi(i,x)*phi(j,x-y),x=y..1)*phi(p,y),y=0..1));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSZjcGx1c0c2ImYqNiVJImlHRiVJImpHRiVJInBHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJS1JKXNpbXBsaWZ5R0YlNiMtSSRpbnRHRiU2JComLUYyNiQqJi1JJHBoaUdGJTYkOSRJInhHRiUiIiItRjk2JDklLCZGPEY9SSJ5R0YlISIiRj0vRjw7RkJGPUY9LUY5NiQ5JkZCRj0vRkI7IiIhRj1GJUYlRiU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cminus := (i,j,p) -&gt; simplify(int(int(phi(i,x)*phi(j,x-y),x=0..y+1)*phi(p,y+1),y=-1..0));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSdjbWludXNHNiJmKjYlSSJpR0YlSSJqR0YlSSJwR0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSlzaW1wbGlmeUdGJTYjLUkkaW50R0YlNiQqJi1GMjYkKiYtSSRwaGlHRiU2JDkkSSJ4R0YlIiIiLUY5NiQ5JSwmRjxGPUkieUdGJSEiIkY9L0Y8OyIiISwmRkJGPUY9Rj1GPS1GOTYkOSZGR0Y9L0ZCO0ZDRkZGJUYlRiU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">cminus(1,1,1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMsJCokIiIkIyIiIiIiIyNGJyIiJg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Digits := 30;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSdEaWdpdHNHNiIiI0k=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"># Note that 
#          cplus(i,j,p) = <Font opaque="false">(-1)**(i+j+p) * cminus(i,j,p)</Font>
#          cplus(i,j,p) = (-1)**(i+j)   * cplus(j,i,p)</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">fd := fopen("autocorr_plus.txt",WRITE);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+SSNmZEc2IiIiIQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">for i from 0 to 34 do
   print("doing ",i);
   for j from 0 to i do
       for p from 0 to (i+j+1) do
          c := eval(cplus(i,j,p));
          if (c &lt;&gt; 0) then
             fprintf(fd,"%d %d %d %.17e\n",i,j,p,evalf(c));
             fflush(fd); 
          fi;
       od;
   od;
od;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIh</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIi</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIj</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIk</Equation></Text-field><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIl</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIm</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIn</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIo</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIp</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiIq</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM1</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM2</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM3</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM4</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM5</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM6</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM7</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM8</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM9</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM+</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiM/</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiNA</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiNB</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiNC</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiND</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiNE</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiNF</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiNG</Equation></Text-field></Output><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiRRJ2RvaW5nfjYiIiNH</Equation></Text-field></Output><Output><Text-field layout="Warning" style="Warning">Warning,  computation interrupted</Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">close(fd);</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">phi(1,x);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMqJi0lJXNxcnRHNiMiIiQiIiIsJiUieEciIiMhIiJGKEYo</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">with(orthopoly):</Text-field></Input></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">int(phi(1,x)*phi(0,x),x=0..1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMiIiE=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">phi(2,x);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMqJi0lJXNxcnRHNiMiIiYiIiIsJiokKSwmJSJ4RyIiIyEiIkYoRi5GKCMiIiRGLiNGL0YuRihGKA==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">phi(0,x);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMiIiI=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">phi(0,0.2);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMiIiI=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalf(phi(1,0.2));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkISsmW0kjUjUhIio=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalf(phi(2,0.2));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIis3PkZXKikhIzY=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalf(phi(3,0.2));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIis/WnFDJiohIzU=</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalf(phi(4,0.2));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkISsrKytDNyEiKg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">evalf(phi(5,0.2));</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIit6Z1xpXSEjNQ==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">a := 10.0;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+JSJhRyQiJSs1ISIi</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">int(exp(-a*x*x)*x^21,x=0..1);</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiMkIjUrKysrKysrUzk9ISNO</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Digits := 20;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+JSdEaWdpdHNHIiM/</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">int(exp(-b*x*x)*(x-l),x=l..l+1);</Text-field></Input><Output><Text-field layout="_pstyle12" style="2D Output"><Equation style="2D Output">NiMsJComLCoqJi0lJGV4cEc2IywkKiYpLCYlImxHIiIiRi9GLyIiI0YvJSJiR0YvISIiRi8tJSVzcXJ0RzYjRjFGL0YyKi5GJ0YvRi5GLy1GNDYjJSNQaUdGLy0lJGVyZkc2IywmKiZGM0YvRi5GL0YvKiRGM0YvRi9GL0YxRi8tRig2I0YrRi9GMiomLUYoNiMsJComRjFGLylGLkYwRi9GMkYvRjNGL0YvKi5GQ0YvRi5GL0Y3Ri8tRjs2I0Y+Ri8tRig2I0ZGRi9GMUYvRi9GLyokKUYxIyIiJEYwRi9GMiNGL0Yw</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">int(exp(-a*x*x)*(x-0)^21,x=0..1);</Text-field></Input><Output><Text-field layout="_pstyle12" style="2D Output"><Equation style="2D Output">NiMkIltzTXpwTUBNaCEpPmEieSMpMzFEdiEpNCMpKjQxWlQoPmJxVyZvJ29bWV8oKltBZCFcWF5TVyEpKnlkJHoqKioqKioqKioqKioqKioqKioqKioqKipSOT0hJFYi</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">a := 100.0;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+JSJhRyQiJSs1ISIi</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input">Digits := 128;</Text-field></Input><Output><Text-field layout="Maple Output" style="2D Output"><Equation style="2D Output">NiM+JSdEaWdpdHNHIiRHIg==</Equation></Text-field></Output></Group><Group><Input><Text-field layout="Normal" prompt="&gt; " style="Maple Input"/></Input></Group><Text-field/><Text-field/></Worksheet>