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Simplified 4D Moffat

(%i1) | f4s4(x4,x3,x2,x1,alpha,beta) := ( 1 + (x1^2 + x2^2 + x3^2 + x4^2)/ alpha ^2 )^(-beta);

(%i2) | f4s3(x3,x2,x1,alpha,beta) := defint( f4s4(x4,x3,x2,x1,alpha,beta), x4, -inf, inf );

(%i3) | f4s2(x2,x1,alpha,beta) := defint( f4s3(x3,x2,x1,alpha,beta), x3, -inf, inf );

(%i4) | f4s1(x1,alpha,beta) := defint( f4s2(x2,x1,alpha,beta), x2, -inf, inf );

(%i5) | f4s0(alpha,beta) := defint( f4s1(x1,alpha,beta), x1, -inf, inf );

(%i6) | norm(alpha, beta) := factor(makegamma(ratsimp(f4s0(alpha,beta))));

(%i7) | killcontext(initial); assume( alpha > 0, beta > 0, beta < 0.5 ); norm(alpha,beta);

(%i10) | killcontext(initial); assume( alpha > 0, equal(beta,0.5)); norm(alpha,beta);

(%i13) | killcontext(initial); assume( alpha > 0, beta > 0.5, beta < 1 ); norm(alpha,beta);

(%i16) | killcontext(initial); assume( alpha > 0, equal(beta,1)); norm(alpha,beta);

(%i19) | killcontext(initial); assume( alpha > 0, beta > 1, beta < 3/2 ); norm(alpha,beta);

(%i22) | killcontext(initial); assume( alpha > 0, equal(beta,3/2) ); norm(alpha,beta);

(%i25) | killcontext(initial); assume( alpha > 0, beta > 3/2, beta < 2 ); norm(alpha,beta);

(%i28) | killcontext(initial); assume( alpha > 0, equal(beta,2) ); norm(alpha,beta);

(%i31) | killcontext(initial); assume( alpha > 0, beta > 2, beta < 3 ); norm(alpha,beta);

(%i34) | killcontext(initial); assume( alpha > 0, equal(beta,3)); norm(alpha,beta);

(%i37) | killcontext(initial); assume( alpha > 0, beta > 3, beta < 7/2 ); norm(alpha,beta);

(%i40) | killcontext(initial); assume( alpha > 0, equal(beta,7/2) ); norm(alpha,beta);

(%i43) | killcontext(initial); assume( alpha > 0, beta > 7/2, beta < 4 );norm(alpha,beta);

(%i46) | killcontext(initial); assume( alpha > 0, equal(beta, 4) );norm(alpha,beta);

(%i49) | killcontext(initial); assume( alpha > 0, beta > 4 );norm(alpha,beta);

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