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Results tagged with real-analysis
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user 170778
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
4
votes
1
answer
253
views
How can a divergent nested radical be regularized (analogously to Cesaro sum regularization ...
The infinite series $1-1+1-1+\cdots$ diverges because the sequence of partial sums, $1,0,1,0,\ldots$ has no limit. However, it is well know that we can get around this problem in a number of ways; th …
- 1,422
3
votes
Evaluating a sinusoidal series
Those are very close to the spherical Bessel functions of the first kind
$$f_{n}=\left(\frac{-z}{2}\right)^{n}j_{n}(z)=(-1)^{n}\frac{\sqrt{\pi}}{2}\left(\frac{z}{2}\right)^{n-\frac{1}{2}}J_{n+\frac{1} …
- 1,422