I am given a coefficient to estimate as a assignment question. But I am unable to think how it must be true. Notations Let $l$ belongs to $\{1, 2,\ldots,a\}$ and $j$ belongs to $\{0,1,\ldots,n\}$. Assume that this equation holds $$ c_{l,j,n}=\frac{1}{2\pi i}\int_{|z+j+1|=\frac{1}{2}} R_n(t) (z+j+1)^{l-1}\mathrm{d}z. $$ where $$ R_n(t) = \frac{(n!)^{a-2r} ×(t-rn+1)_{rn} (t+n+2)_{rn}}{(t+1)_{n+1}}. $$ Also note […]

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## Unable to deduce an inequality related to an integral

- Post author By Q+A Expert
- Post date March 26, 2020
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- Tags ...a} and j belongs to {0, \ldots, 1, 2, I am given a coefficient to estimate as a assignment question. But I am unable to think how it must be true. Notations -> Let l belongs to {, I am unable to think how to deduce next step which is (adding it's image) -> |$c_{l, j, n} . Assume that this equation holds ->$c_{l, n}=\frac{1}{2\pi i}\int_{|z+j+1|=\frac{1}{2}} R_n(t) (z+j+1)^{l-1}\mathrm{d}z. $$ where $$ R_n(t) = \frac{(n!)^{a-2r} ×(t-rn+1)_{rn} (t+n+2)_, n}=D_{a-l}(R_n(t)(t+j+1)^a)_{t=-j-1}. $$ These identities are to be used but have already been proved by me. $$ \begin{split} |(z-rn+1)_{rn}|, n}$|$\leq$.... I don't know how to deduce this from (1) and related results given and how did integral just vanished?