matlab - Problems with symsum() function in Symbolic Math Toolbox -

i'm having problems when using symsum function in matlab's symbolic math toolbox. code should returning:

ans = sin(x) + x*cos(x) - x^2 / 2 * sin(x) 

i think has symbolic variables, i'm new matlab appreciated.

here's code:

syms x i; f(x) = sin(x);  symsum(x^i/factorial(i)*diff(f,x,i), i, 0, 2) 

which returns 0 instead of correct result indicated above.

this occurs because diff(f,x,i) evaluates zero. when using symsum, need aware that, matlab function, input arguments evaluated before being passed in. use for loop (sym/diff not vectorized in third argument – see below):

syms x y; f(x) = sin(x); n = 0:2; y = 0; = n     y = y+x^i/factorial(i)*diff(f,x,i); end 

alternatively, try form (in case, 3 indexes, above more efficient):

syms x y; f(x) = sin(x); n = 0:2; % increasing orders of differentiation y = diff(f,x,n(1)); yi = [y(x) zeros(1,length(n)-1)]; % index array, yi cannot symfun = 2:length(n)     % calculate next derivative previous     yi(i) = diff(yi(i-1),x,n(i)-n(i-1)); end % convert yi symfun output symfun y = sum(x.^n./factorial(n).*symfun(yi,x)); 

why diff(f,x,i) evaluate 0 though i symbolic? documentation sym/diff:

diff(s,n), positive integer n, differentiates s n times.
diff(s,'v',n) , diff(s,n,'v') acceptable.

in other words, function doesn't support symbolic variables specify order of integration. order, n (or i in code) limited scalar. mupad's related functions have similar limitations unfortunately.

in opinion, sym/diff should throw error if has limitation rather returning garbage. i'd recommend file service request mathworks report issue. request function updated handle symbolic variables order of integration input.