Simplified 2D Moffat
(%i1) | f2s2(x2,x1,alpha,beta) := ( 1 + (x1^2 + x2^2)/ alpha ^2 )^(-beta); |
(%i2) | f2s1(x1,alpha,beta) := defint( f2s2(x2,x1,alpha,beta), x2, -inf, inf ); |
(%i3) | f2s0(alpha,beta) := defint( f2s1(x1,alpha,beta), x1, -inf, inf ); |
(%i4) | norm(alpha, beta) := factor(makegamma(ratsimp(f2s0(alpha,beta)))); |
(%i5) | killcontext(initial); assume( alpha > 0, beta > 0, beta < 0.5 ); norm(alpha,beta); |
(%i8) | killcontext(initial); assume( alpha > 0, equal(beta,0.5)); norm(alpha,beta); |
(%i11) | killcontext(initial); assume( alpha > 0, beta > 0.5, beta < 1 ); norm(alpha,beta); |
(%i14) | killcontext(initial); assume( alpha > 0, equal(beta,1)); norm(alpha,beta); |
(%i50) | killcontext(initial); assume( alpha > 0, beta > 1, beta < 3 ); norm(alpha,beta); |
(%i56) | killcontext(initial); assume( alpha > 0, equal(beta,3) ); norm(alpha,beta); |
(%i53) | killcontext(initial); assume( alpha > 0, beta > 3 ); norm(alpha,beta); |