Simplified 5D Moffat

(%i1) f4s5(x5,x4,x3,x2,x1,alpha,beta) := ( 1 + (x1^2 + x2^2 + x3^2 + x4^2 + x5^2)/ alpha ^2 )^(-beta);

Result

(%i2) f4s4(x4,x3,x2,x1,alpha,beta) := defint( f4s5(x5,x4,x3,x2,x1,alpha,beta), x5, -inf, inf );

Result

(%i3) f4s3(x3,x2,x1,alpha,beta) := defint( f4s4(x4,x3,x2,x1,alpha,beta), x4, -inf, inf );

Result

(%i4) f4s2(x2,x1,alpha,beta) := defint( f4s3(x3,x2,x1,alpha,beta), x3, -inf, inf );

Result

(%i5) f4s1(x1,alpha,beta) := defint( f4s2(x2,x1,alpha,beta), x2, -inf, inf );

Result

(%i6) f4s0(alpha,beta) := defint( f4s1(x1,alpha,beta), x1, -inf, inf );

Result

(%i7) norm(alpha, beta) := factor(makegamma(ratsimp(f4s0(alpha,beta))));

Result

(%i8) killcontext(initial); assume( alpha > 0, beta > 0, beta < 0.5 ); norm(alpha,beta);

Result

(%i11) killcontext(initial); assume( alpha > 0, equal(beta,0.5)); norm(alpha,beta);

Result

(%i14) killcontext(initial); assume( alpha > 0, beta > 0.5, beta < 1 ); norm(alpha,beta);

Result

(%i17) killcontext(initial); assume( alpha > 0, equal(beta,1)); norm(alpha,beta);

Result

(%i20) killcontext(initial); assume( alpha > 0, beta > 1, beta < 3/2 ); norm(alpha,beta);

Result

(%i23) killcontext(initial); assume( alpha > 0, equal(beta,3/2) ); norm(alpha,beta);

Result

(%i26) killcontext(initial); assume( alpha > 0, beta > 3/2, beta < 2 ); norm(alpha,beta);

Result

(%i29) killcontext(initial); assume( alpha > 0, equal(beta,2) ); norm(alpha,beta);

Result

(%i32) killcontext(initial); assume( alpha > 0, beta > 2, beta < 5/2 ); norm(alpha,beta);

Result

(%i35) killcontext(initial); assume( alpha > 0, equal(beta, 5/2) ); norm(alpha,beta);

Result

(%i38) killcontext(initial); assume( alpha > 0, beta > 5/2, beta < 3 ); norm(alpha,beta);

Result

(%i41) killcontext(initial); assume( alpha > 0, equal(beta,3)); norm(alpha,beta);

Result

(%i44) killcontext(initial); assume( alpha > 0, beta > 3, beta < 7/2 ); norm(alpha,beta);

Result

(%i47) killcontext(initial); assume( alpha > 0, equal(beta,7/2) ); norm(alpha,beta);

Result

(%i50) killcontext(initial); assume( alpha > 0, beta > 7/2, beta < 4 );norm(alpha,beta);

Result

(%i53) killcontext(initial); assume( alpha > 0, equal(beta, 4) );norm(alpha,beta);

Result

(%i56) killcontext(initial); assume( alpha > 0, beta > 4, beta < 9/2 );norm(alpha,beta);

Result

(%i59) killcontext(initial); assume( alpha > 0, equal(beta, 9/2 ) );norm(alpha,beta);

Result

(%i62) killcontext(initial); assume( alpha > 0, beta > 9/2 );norm(alpha,beta);

Result


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