Divergent Integrals

List of divergent integrals.

$\Gamma(z)$ denotes the Gamma function.
$\Gamma'(z)$ denotes the derivative of the Gamma function.
$K(z)$ denotes the K-function.
$K'(z)$ denotes the derivative of the K-function.
$\psi^{(0)}(z)$ denotes the Digamma function.
$\psi^{(1)}(z)$ denotes the Trigamma function.
$\zeta(z)$ denotes the Riemann zeta function.
$\zeta'(z)$ denotes the derivative of the Riemann zeta function.
$\xi(z)$ denotes the Riemann xi function.
$\xi'(z)$ denotes the derivative of the Riemann xi function.
$\eta(z)$ denotes the Dirichlet eta function.
$\eta'(z)$ denotes the derivative of the Dirichlet eta function.
$P(z)$ denotes the prime zeta function.
$P'(z)$ denotes the derivative of the prime zeta function.
$\theta_3(z,q)$ denotes the Jacobi theta_3 function.

$H_n$ denotes the n-th harmonic number (with $H_0 = 0$ ).
$H_n'$ denotes the n-th alternating harmonic number (with $H_0' = 0$ ).
$\displaystyle H_{n,r} = \sum_{m=1}^{n} \dfrac{1}{m^r}$ denotes the n-th generalized harmonic number of order r (with $H_{0,r} = 0$ ).
$\displaystyle H_n^{(r)} = \sum_{m=1}^{n} H_m^{(r-1)}$ denotes the n-th hyperharmonic number of order r (with $H_n^{(1)} = H_n$ ).