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Simplified 3D Moffat

(%i1) | f3s3(x3,x2,x1,alpha,beta) := ( 1 + (x1^2 + x2^2 +x3^2)/ alpha ^2 )^(-beta);

(%i2) | f3s2(x2,x1,alpha,beta) := defint( f3s3(x3,x2,x1,alpha,beta), x3, -inf, inf );

(%i3) | f3s1(x1,alpha,beta) := defint( f3s2(x2,x1,alpha,beta), x2, -inf, inf );

(%i4) | f3s0(alpha,beta) := defint( f3s1(x1,alpha,beta), x1, -inf, inf );

(%i5) | norm(alpha, beta) := factor(makegamma(ratsimp(f3s0(alpha,beta))));

(%i29) | killcontext(initial); assume( alpha > 0, beta > 0, beta < 0.5 ); norm(alpha,beta);

(%i32) | killcontext(initial); assume( alpha > 0, equal(beta,0.5)); norm(alpha,beta);

(%i35) | killcontext(initial); assume( alpha > 0, beta > 0.5, beta < 1 ); norm(alpha,beta);

(%i40) | killcontext(initial); assume( alpha > 0, equal(beta,1)); norm(alpha,beta);

(%i43) | killcontext(initial); assume( alpha > 0, beta > 1, beta < 3/2 ); norm(alpha,beta);

(%i46) | killcontext(initial); assume( alpha > 0, equal(beta,3/2) ); norm(alpha,beta);

(%i49) | killcontext(initial); assume( alpha > 0, beta > 3/2, beta < 3 ); norm(alpha,beta);

(%i70) | killcontext(initial); assume( alpha > 0, equal(beta,3)); norm(alpha,beta);

(%i55) | killcontext(initial); assume( alpha > 0, beta > 3, beta < 7/2 ); norm(alpha,beta);

(%i64) | killcontext(initial); assume( alpha > 0, equal(beta,7/2) ); norm(alpha,beta);

(%i67) | killcontext(initial); assume( alpha > 0, beta > 7/2 );norm(alpha,beta);

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