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Question Number 202592 by Calculusboy last updated on 30/Dec/23

$$\mathit{I}\mathit{f}{\mathit{I}}_{\mathit{n}}\mathit{d}\mathit{e}\mathit{n}\mathit{o}\mathit{t}\mathit{e}\mathit{s}\int {\mathit{z}}^{\mathit{n}}{\mathit{e}}^{\frac{1}{\mathit{z}}}\mathit{d}\mathit{z},\mathit{t}\mathit{h}\mathit{e}\mathit{n}\mathit{s}\mathit{h}\mathit{o}\mathit{w}\mathit{t}\mathit{h}\mathit{a}\mathit{t}$$$$(\mathit{n}+1)!{\mathit{I}}_{\mathit{n}}={\mathit{I}}_0+{\mathit{e}}^{\frac{1}{\mathit{z}}}(1\cdot !{\mathit{z}}^2+2\cdot !{\mathit{z}}^3+\cdot \cdot \cdot +\mathit{n}!\cdot {\mathit{z}}^{\mathit{n}+1})$$$$$$

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