Sum of series with differentaition

%% I am try to sum a series with respect to k, where function f has 2*k-1 times derivative too. As below program i am using and then error occured.

sysms k t

f = zeta(2*k)*(4^k-2)/4^k*diff(t^(-1/2),t,2*k-1)

pretty(f)

F = symsum(f,k,1,10)

%% I am facing error as

%%Error using sym/diff (line 71)

%%The second and third arguments must either be variables or a variable and a nonnegative integer specifying the number of differentiations.

%%Error in main (line 13)

%%f = zeta(2*k)*(4^k-2)/4^k*diff(t^(-1/2),t,2*k-1)

Answer 1

[John D'Errico]

There is no reason to use symsum on this.

syms t
f = sym(0);
for k = 1:10
  f = f + zeta(2*k).*(4.^k-2)/4.^k*diff(t^(-1/2),t,2*k-1);
end
vpa(f,5)
ans =
- 0.41123/t^(3/2) - 1.7757/t^(7/2) - 29.105/t^(11/2) - 1051.8/t^(15/2) - 67239.0/t^(19/2) - 6.7119e6/t^(23/2) - 9.6501e8/t^(27/2) - 1.8891e11/t^(31/2) - 4.8314e13/t^(35/2) - 1.5642e16/t^(39/2)

diff cannot handle a sumbolic order of dfferentiation anyway, so a simple loop is entirely adequate.

[SHARAD KUMAR UPADHYAY]

Thank you for your suggestion, it is helpful for me.

[SHARAD KUMAR UPADHYAY]

%% when i am trying this

syms y a t Q

FT = sym(0 );

y= a/t

for k = 1:5

FT = FT + zeta(2*k).*(4.^k-2)/4.^k*diff(y^(-1/2),y,2*k-1 );

end

vpa(FT,5 )

chi=(y^(1/2)+FT)*t^(1/2)/Q;

vpa(chi,3)

%%Then I found the error as

%%Error using sym/diff (line 71)

%%The second and third arguments must either be variables or a variable and a nonnegative integer specifying the number of differentiations.

%%Error in Im_Xi (line 6)

%%FT = FT + zeta(2*k).*(4.^k-2)/4.^k*diff(y^(-1/2),y,2*k-1 );

[Walter Roberson]

your y is an expression not a variable . you cannot differentiate with respect to an expression