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Category: Integration

Question-218952

Question Number 218952 by Spillover last updated on 17/Apr/25 Commented by MathematicalUser2357 last updated on 17/Apr/25 $$\mathrm{What}\:\mathrm{kind}\:\mathrm{of}\:\mathrm{function}\:\mathrm{is}\:\mathrm{Ti}_{\mathrm{2}} ???\:\mathrm{Can}\:\mathrm{someone}\:\mathrm{help}\:\mathrm{me}\:\mathrm{before}\:\mathrm{I}\:\mathrm{eat}\:\mathrm{that}\:\mathrm{question}??? \\ $$ Commented by SdC355 last updated…

Calculate-the-following-integral-xJ-0-x-2-y-2-J-1-y-2-z-2-J-2-z-2-x-2-e-x-2-y-2-z-2-dxdydz-where-J-n-u-is-the-Bas

Question Number 218879 by Nicholas666 last updated on 16/Apr/25 $$ \\ $$$$\:\:\:\boldsymbol{{Calculate}}\:\boldsymbol{{the}}\:\boldsymbol{{following}}\:\boldsymbol{{integral}};\:\:\:\:\:\: \\ $$$$\:\:\int_{−\infty} ^{\infty} \int_{−\infty} ^{\infty} \int_{−\infty} ^{\infty} \boldsymbol{{xJ}}_{\mathrm{0}} \left(\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} }\right)\boldsymbol{{J}}_{\mathrm{1}} \left(\sqrt{\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}}…

Calculate-the-following-integral-0-0-0-J-ax-J-by-J-cz-x-2-y-2-z-2-e-p-x-2-y-2-z-2-dxdydz-where-J-u-is-the-Bassel-f

Question Number 218872 by Nicholas666 last updated on 16/Apr/25 $$ \\ $$$$\:\boldsymbol{{Calculate}}\:\boldsymbol{{the}}\:\boldsymbol{{following}}\:\boldsymbol{{integral}}; \\ $$$$\:\:\:\int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \int_{\mathrm{0}} ^{\infty} \:\frac{\boldsymbol{{J}}_{\boldsymbol{\alpha}} \left(\boldsymbol{{ax}}\right)\boldsymbol{{J}}_{\boldsymbol{\beta}} \left(\boldsymbol{{by}}\right)\boldsymbol{{J}}_{\boldsymbol{\gamma}} \left(\boldsymbol{{cz}}\right)}{\:\sqrt{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} +\boldsymbol{{z}}^{\mathrm{2}}…

evaluate-the-following-integral-in-closed-form-or-express-it-in-terms-of-known-special-functions-K-i-at-J-bt-1-dt-where-K-i-z-is-the-modified-Bess

Question Number 218866 by Nicholas666 last updated on 16/Apr/25 $$ \\ $$$$\:\:\:{evaluate}\:{the}\:{following}\:{integral}\:{in}\:{closed}\:{form}\:{or}\:{express} \\ $$$$\:{it}\:{in}\:{terms}\:{of}\:{known}\:{special}\:{functions};\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\int_{ } ^{\infty} \boldsymbol{{K}}_{\boldsymbol{{i}\lambda}} \left(\boldsymbol{{at}}\right)\boldsymbol{{J}}_{\boldsymbol{\nu}} \left(\boldsymbol{{bt}}\right)^{\boldsymbol{\mu}−\mathrm{1}} \boldsymbol{{dt}} \\ $$$$\:\boldsymbol{{where}}; \\…

0-x-2-cos-x-cosh-2x-cos-x-2x-2-e-4x-2e-2x-cos-x-1-dx-lemma-k-1-cos-kx-p-k-p-cos-x-1-p-2-2p-cos-x-1-p-gt-1-

Question Number 218748 by MrGaster last updated on 15/Apr/25 $$\int_{\mathrm{0}} ^{\infty} \frac{{x}^{\mathrm{2}} \mathrm{cos}\:{x}}{\mathrm{cosh}\:\mathrm{2}{x}−\mathrm{cos}\:{x}}−\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{e}^{\mathrm{4}{x}} −\mathrm{2}{e}^{\mathrm{2}{x}} \mathrm{cos}\:{x}+\mathrm{1}}{dx},\mathrm{lemma}:\underset{{k}=\mathrm{1}} {\overset{+\infty} {\sum}}\frac{\mathrm{cos}\:{kx}}{{p}^{{k}} }=\frac{\mathrm{p}\:\mathrm{cos}\:{x}−\mathrm{1}}{{p}^{\mathrm{2}} −\mathrm{2}{p}\:\mathrm{cos}\:{x}+\mathrm{1}},{p}>\mathrm{1} \\ $$ Answered by MrGaster…