SandorSzabo

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19 years, 341 days

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These are questions asked by SandorSzabo

My colleague at the university next week give a lecture where he tells about the Hardy-Ramanujan partition functions, the usual

notations are p(n) and q(n). He asked me, could I calculate by Maple a definite integral, because the answer was yes, then he

would say "by Maple".  I tried it in different ways, but no success. Could someone calculate it?

The exact result is  -1/2 ln (2 Pi) .

I have the expression

(r(r+(1/2)*s))(sin(t)/(r+(1/2)*s)+(diff(y(x), x))/(r^2+(1/2)*rs))

and I want to obtain

r*sin(t)+diff(y(x),x)

I tried expand,collect,combine without success.

Hopefully I missed something and there is a simple solution.

Thanks in advance.

                                       Sandor

I typed in

series( 1/4*sqrt(2)*sqrt(Pi)*exp(-1/2)*(erf(1/2*sqrt(2)*x-1/2*I*sqrt(2))+erf(1/2*sqrt(2)*x+1/2*I*sqrt(2)))*exp(1/2*x^2),x);

I used  exp to avoid a pitfall.

Maple says

I obtained the following result

> dsolve({diff(y(x), x, x)+e^x*(diff(y(x), x))+(1+x^2)*y(x) = 0, y(0) = 1, (D(y))(0) = 0}, y(x), series);
 
y(x) = 1-(1/2)*x^2+(1/6)*x^3+((1/12)*ln(e)-1/12)*x^4+O(x^5));

I have a proc and I want to test if the function is odd.

The following is wrong, but could you modify it to work well?

smth:=proc(f::algebraic,x)

if  simplify( f(x)+f(-x) )=0

then print("f is odd");

end if;

end proc;

In the proc argument there is x because x is the variable of f,  for example  f  may have other

parameters,   (in mathematical notation)  f(x)=ax+3.

Thanks,       Sandor

 

 

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