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These are questions asked by radaar

Integral is not evaluated. 



In the first one I used hypergeometric function where the number is converged. Now using the series expansion of hypergeometric function I rewrite the equation as in the 2nd and 3rd case. But here it is not converging. I expect the same answer as in the first case i.e 0.14042. Thank you



In the following problem at two example are given. For Z=2 the sum is converging whereas at Z=4 it is not converging. Thank you



In the following file when p is a fraction other than 1/2 the integral is not evaluated. Please help




restart; Digits := 7; r := 2.5; Q := proc (n) options operator, arrow; int(simplify(1/(x*r^2*cos(x-y)+z*r^2*sin(z-y))^n, symbolic), y = 0 .. Pi) end proc; HH := eval(Q(5))

int(0.1048576e-3/(x^5*cos(x-1.*y)^5-5.*x^4*cos(x-1.*y)^4*z*sin(-1.*z+y)+10.*x^3*cos(x-1.*y)^3*z^2-10.*x^3*cos(x-1.*y)^3*z^2*cos(-1.*z+y)^2-10.*x^2*cos(x-1.*y)^2*z^3*sin(-1.*z+y)+10.*x^2*cos(x-1.*y)^2*z^3*sin(-1.*z+y)*cos(-1.*z+y)^2+5.*x*cos(x-1.*y)*z^4-10.*x*cos(x-1.*y)*z^4*cos(-1.*z+y)^2+5.*x*cos(x-1.*y)*z^4*cos(-1.*z+y)^4-1.*z^5*sin(-1.*z+y)+2.*z^5*sin(-1.*z+y)*cos(-1.*z+y)^2-1.*z^5*sin(-1.*z+y)*cos(-1.*z+y)^4), y = 0 .. Pi)




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