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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);

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