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Results tagged with ca.classical-analysis-and-odes
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user 466773
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
9
votes
1
answer
618
views
Infinite series with inverse trigonometric functions
Consider the infinite series
$$
F(s)=\sum_{k=1}^\infty \frac{1}{k^{2s+1} \sin(k \pi \sqrt{2})}
$$
Prudnikov Vol.1 , gives a result for this sum in 5.4.16.13 for $s=1.$
$$
F(1)=-\frac{13 \pi^3}{360 \sq …
- 91