is-k-J-k-k-l-0-1-l-l-l-k-2-2l-l-0-k-1-l-l-l-k-2-2l-k-

Question Number 219359 by SdC355 last updated on 23/Apr/25

is Σ_(k=−∞) ^∞ J_ν (k)= Σ_(k=−∞) ^∞ Σ_(l=0) ^∞ (((−1)^l )/(l!(l+ν)!))((k/2))^(2l+ν) =Σ_(l=0) ^∞ Σ_(k=−∞) ^∞ (((−1)^l )/(l!(l+ν)!))((k/2))^(2l+k) ??

$$\mathrm{is}\:\underset{{k}=−\infty} {\overset{\infty} {\sum}}\:{J}_{\nu} \left({k}\right)= \\ $$$$\underset{{k}=−\infty} {\overset{\infty} {\sum}}\:\underset{{l}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{l}} }{{l}!\left({l}+\nu\right)!}\left(\frac{{k}}{\mathrm{2}}\right)^{\mathrm{2}{l}+\nu} =\underset{{l}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{{k}=−\infty} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{{l}} }{{l}!\left({l}+\nu\right)!}\left(\frac{{k}}{\mathrm{2}}\right)^{\mathrm{2}{l}+{k}} ?? \\ $$

Facebook Tweet Pin

is-k-J-k-k-l-0-1-l-l-l-k-2-2l-l-0-k-1-l-l-l-k-2-2l-k-

Leave a Reply Cancel reply