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i-generalized-Bessel-function-s-Laplace-Transform-L-TJ-z-s-s-2-1-s-2-1-s-0-R-L-T-Y-z-cot-pi-s-s-2-1-s-2-1-csc-pi-s-s-2-1

Question Number 212765 by issac last updated on 23/Oct/24 $$\mathrm{i}\:\:\mathrm{generalized}\:\boldsymbol{\mathrm{Bessel}}\:\boldsymbol{\mathrm{function}}'\mathrm{s} \\ $$$$\mathrm{Laplace}\:\mathrm{Transform} \\ $$$$\mathrm{L}.\mathrm{T}{J}_{\nu} \left({z}\right)=\frac{\left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{−\nu} }{\:\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}}\:,\:{s}\in\left[\mathrm{0},\infty\right)\:,\:\nu\in\mathbb{R} \\ $$$$\mathrm{L}.\mathrm{T}\:{Y}_{\nu} \left({z}\right)=\frac{\mathrm{cot}\left(\pi\nu\right)\left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{−\nu} }{\:\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}}−\frac{\mathrm{csc}\left(\pi\nu\right)\left({s}+\sqrt{{s}^{\mathrm{2}} +\mathrm{1}}\right)^{\nu}…

prove-the-Following-Equation-J-z-and-Y-z-are-Bessel-function-J-1-2-z-1-1-Y-1-2-z-Y-1-2-z-1-J-1-2-z-Z-Do-Not-prove-using-the-equations-pres

Question Number 212648 by issac last updated on 20/Oct/24 $$\mathrm{prove}\:\mathrm{the}\:\mathrm{Following}\:\mathrm{Equation}. \\ $$$$\:{J}_{\nu} \left({z}\right)\:\mathrm{and}\:{Y}_{\nu} \left({z}\right)\:\mathrm{are}\:\:\mathrm{Bessel}\:\mathrm{function} \\ $$$${J}_{−\nu−\frac{\mathrm{1}}{\mathrm{2}}} \left({z}\right)=\left(−\mathrm{1}\right)^{\nu+\mathrm{1}} {Y}_{\nu+\frac{\mathrm{1}}{\mathrm{2}}} \left({z}\right) \\ $$$${Y}_{−\nu−\frac{\mathrm{1}}{\mathrm{2}}} \left({z}\right)=\left(−\mathrm{1}\right)^{\nu} {J}_{\nu+\frac{\mathrm{1}}{\mathrm{2}}} \left({z}\right) \\…

lim-n-1-2-n-2-1-2-3-n-2-2-n-n-1-n-2-n-

Question Number 212627 by MrGaster last updated on 19/Oct/24 $$ \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\sqrt{\mathrm{1}\centerdot\mathrm{2}}}{{n}^{\mathrm{2}} +\mathrm{1}}+\frac{\sqrt{\mathrm{2}\centerdot\mathrm{3}}}{{n}^{\mathrm{2}} +\mathrm{2}}+\ldots+\frac{\sqrt{{n}\left({n}+\mathrm{1}\right)}}{{n}^{\mathrm{2}} +{n}}\right) \\ $$ Answered by mehdee7396 last updated on 19/Oct/24…

lim-n-0-k-1-n-k-2-3k-2-k-2-2k-1-1-n-

Question Number 212618 by MrGaster last updated on 19/Oct/24 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\underset{{k}=\mathrm{1}} {\overset{{n}} {\prod}}\frac{{k}^{\mathrm{2}} +\mathrm{3}{k}+\mathrm{2}}{{k}^{\mathrm{2}} +\mathrm{2}{k}+\mathrm{1}}\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ Commented by mehdee7396 last updated on…

Verify-the-equation-tan-nx-k-1-n-1-2-1-k-1-n-2k-1-tan-2k-1-x-k-0-n-2-1-k-n-2k-tan-2k-x-

Question Number 212615 by MrGaster last updated on 19/Oct/24 $$\mathrm{Verify}\:\mathrm{the}\:\mathrm{equation}:\mathrm{tan}\:{nx}=\underset{{k}=\mathrm{1}} {\overset{\left[\frac{{n}+\mathrm{1}}{\mathrm{2}}\right]} {\sum}}\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} \begin{pmatrix}{{n}}\\{\mathrm{2}{k}−\mathrm{1}}\end{pmatrix}\:\mathrm{tan}^{\mathrm{2}{k}−\mathrm{1}} {x}/\underset{{k}=\mathrm{0}} {\overset{\left[\frac{{n}}{\mathrm{2}}\right]} {\sum}}\left(−\mathrm{1}\right)^{{k}} \begin{pmatrix}{{n}}\\{\mathrm{2}{k}}\end{pmatrix}\mathrm{tan}^{\mathrm{2}{k}} {x} \\ $$ Terms of Service Privacy Policy…