  The pursuit of closed forms for infinite series has long been a focal point
of research. In this paper, we contribute to this endeavor by presenting closed
forms for the class of digamma series: \[\sum_{k=1}^\infty
\frac{\psi\left(\frac{2k+2n+5}{4}\right) -
\psi\left(\frac{2k+2n+3}{4}\right)}{(2k + \alpha)^2},\] \[\sum_{k=1}^\infty
(-1)^k \frac{\psi\left(\frac{2k+2n+5}{4}\right) -
\psi\left(\frac{2k+2n+3}{4}\right)}{(2k + \alpha)^2},\] for all non-negative
integers $\alpha$ and $n$. In addition to providing closed forms for these
series, we unveil new identities for various generalized digamma series in the
elegant form $a_0 + a_1 \pi + a_2 \pi^2 + a_3 \pi^3$, where $a_0, \ldots, a_3$
are real-valued constants determined by our formulas. Furthermore, we present
ten definite integrals over the interval $(0, 1)$ that have not been previously
studied in the literature and appear to be nearly impossible to evaluate.
Combining these series and integrals can lead to the discovery of even more new
results. Our findings contribute to the study of closed forms for infinite
series and integrals, offering novel results and potential avenues for further
exploration.
