使用matlab求级数求和

当我在 matlab 中写这个时

syms x;
f=x^3-cos(x);
g=diff(f)

它给出的输出为

g =

3*x^2+正弦(x)

Now I want to generate summation series as

我搜索并找到“symsum”命令，但当我编写以下命令时，它没有执行我所需的任务

syms k
symsum(k^2, 0, 10)
symsum(1/k^2,1,Inf)

它给出的输出为

答：385

ans = pi^2/6

Can you guys guide me how can I genereate the series which produce output as

so that when I give command diff(Sk); it should produce result as or something like that

例如在 Mathematica 中我可以这样做

您的帮助肯定会有很大的帮助。

我查看了 symsum 函数的帮助，你有一个很好的例子，试试这个：

syms x;
syms k real;
symsum(x^k/sym('k!'), k, 0, inf)

This commands evaluate the series , and actually evaluates to . As you can see you have to specify the term of the series with its dependence of 'k'. Then in the symsum command you have to specify that you want to sum over 'k' from 0 to inf.

例如，您可以执行以下操作：

syms x;
syms k real;
ak = (-1)^k*x^(2*k+1)/sym('(2*k+1)!');
sum_ak = symsum(ak, k, 0, inf);     % gives back sin(x)
dak = diff(ak,x);
sum_dak = symsum(dak, k, 0, inf);   % should give back cos(x), but does not
A5 = symsum(ak, k, 0, 5);           % add only the first values of the series
DA5 = symsum(dak, k, 0, 5);         % add the derivated terms of the series

您可以声明多个符号变量 uk 并将它们相加：

syms x;
syms k real;
n = 5;
for i = 0:n
    eval(['syms u',num2str(i),' real;']);
end

A = cell(1,n);
for i=1:n
    A{i} = u0;
    for j=1:i
        eval(['A{i} = A{i} + u',num2str(j),';']);
    end
end
A{3} % check the value of A{i}

希望这可以帮助，