support/moffat/moffat4.html

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<!---------------------------------------------------------->
<!--          Created with wxMaxima version 0.8.5         -->
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<!-- Text cell -->


<P CLASS="comment">
Simplified 4D Moffat
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i1) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
f4s4(x4,x3,x2,x1,alpha,beta) := ( 1 + (x1^2 + x2^2 + x3^2 + x4^2)/ alpha ^2 )^(-beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_0.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i2) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
f4s3(x3,x2,x1,alpha,beta) := defint( f4s4(x4,x3,x2,x1,alpha,beta), x4, -inf, inf );
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_1.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i3) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
f4s2(x2,x1,alpha,beta) := defint( f4s3(x3,x2,x1,alpha,beta), x3, -inf, inf );
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_2.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i4) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
f4s1(x1,alpha,beta) := defint( f4s2(x2,x1,alpha,beta), x2, -inf, inf );
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_3.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i5) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
f4s0(alpha,beta) := defint( f4s1(x1,alpha,beta), x1, -inf, inf );
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_4.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i6) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
norm(alpha, beta) := factor(makegamma(ratsimp(f4s0(alpha,beta))));
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_5.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i7) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, beta > 0, beta < 0.5 ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_6.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i10) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, equal(beta,0.5)); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_7.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i13) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, beta > 0.5, beta < 1 ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_8.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i16) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, equal(beta,1)); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_9.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i19) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, beta > 1, beta < 3/2 ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_10.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i22) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, equal(beta,3/2) ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_11.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i25) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, beta > 3/2, beta < 2 ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_12.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i28) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, equal(beta,2) ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_13.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i31) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, beta > 2, beta < 3 ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_14.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i34) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, equal(beta,3)); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_15.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i37) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, beta > 3, beta < 7/2 ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_16.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i40) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, equal(beta,7/2) ); norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_17.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i43) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, beta > 7/2, beta < 4 );norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_18.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i46) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, equal(beta, 4) );norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_19.png">
</P>


<!-- Code cell -->


<P><TABLE><TR><TD>
  <SPAN CLASS="prompt">
(%i49) 
  </SPAN></TD>
  <TD><SPAN CLASS="input">
killcontext(initial); assume( alpha > 0, beta > 4 );norm(alpha,beta);
  </SPAN></TD>
</TR></TABLE>
  <BR>
  <IMG ALT="Result" SRC="moffat4_img/moffat4_20.png">
</P>

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