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Question Number 97490 by ali_golmakani last updated on 08/Jun/20

$$pleaseproveit$$$$\cos x=J_0\left(x\right)+2\sum _{x-1}{(-1)}^x{J}_{2x}\left(x\right)$$

Answered by smridha last updated on 08/Jun/20

$$\mathit{I}\mathit{t}\mathit{h}\mathit{i}\mathit{n}\mathit{k}\mathit{i}\mathit{t}\mathit{i}\mathit{s}\mathit{n}\mathit{e}\mathit{e}\mathit{d}\mathit{e}\mathit{d}\mathit{t}\mathit{o}\mathit{c}\mathit{h}\mathit{e}\mathit{c}\mathit{k}\mathit{y}\mathit{o}\mathit{u}\mathit{r}$$$$\mathit{q}\mathit{u}\mathit{e}\mathit{s}\mathit{t}\mathit{i}\mathit{o}\mathit{n}$$$$\sum _{\mathit{x}-1}{(-1)}^{\mathit{x}}{\mathit{J}}_{2x}\left(x\right)\mathit{w}\mathit{h}\mathit{a}\mathit{t}\mathit{d}\mathit{o}\mathit{e}\mathit{s}\mathit{i}\mathit{t}\mathit{m}\mathit{e}\mathit{a}\mathit{n}?$$$$\mathit{I}\mathit{t}\mathit{h}\mathit{i}\mathit{n}\mathit{k}{\mathit{J}}_{2\mathit{n}}\left(\mathit{x}\right)\mathit{B}essel{\mathit{f}}^{\mathit{n}}.$$

Commented by ali_golmakani last updated on 08/Jun/20

$$yes$$

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