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Bounds on $\sum_{j=1}^m\frac{\pi^j}{\Gamma(j)(x^2+(j+1/4)^2)}$

During our search of real rooted entire function approximations to Riemann $\Xi$ function, we need to calculate the upper and lower bounds of $$f_m(x):=\sum_{j=1}^m b_j(x):=\sum_{j=1}^m\frac{\pi^j}{\G …
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