1) Have finished writing my article. However, uniform convergence with respect to 'x' still remains unproven.
2) Tried do derive Dominici result. I found that Paley–Wiener theorem can help me with it.
Item 2 is completed. I've derived the result that is a bit different from the Dominici's one. Numerical calculations showed that as my as Dominici's results are correct and are a part of some more general equality. But my result is better as it is correct for all real values of parameters $a$ and $b$! Whereas Dominici's result is correct only for $a+b\leq2\pi$.
Item 1) is completed. I've proved uniform convergence for all my series expansion for Bessel functions.
ReplyDeleteItem 2 is completed. I've derived the result that is a bit different from the Dominici's one. Numerical calculations showed that as my as Dominici's results are correct and are a part of some more general equality. But my result is better as it is correct for all real values of parameters $a$ and $b$! Whereas Dominici's result is correct only for $a+b\leq2\pi$.
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