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AllQuestion and Answers: Page 44

Question Number 219732 Answers: 1 Comments: 0

Question Number 219731 Answers: 1 Comments: 0

Question Number 219730 Answers: 0 Comments: 0

f(w)=∫_0 ^( ∞) ((θ(s−1))/(s(s−1)^α ))e^(−sw) ds θ^ (s)= { ((0 s<0)),((1 s>0)) :}

$${f}\left({w}\right)=\int_{\mathrm{0}} ^{\:\infty} \:\frac{\theta\left({s}−\mathrm{1}\right)}{{s}\left({s}−\mathrm{1}\right)^{\alpha} }{e}^{−{sw}} \:\mathrm{d}{s} \\ $$$$\hat {\theta}\left({s}\right)=\begin{cases}{\mathrm{0}\:\:{s}<\mathrm{0}}\\{\mathrm{1}\:\:{s}>\mathrm{0}}\end{cases} \\ $$

Question Number 219725 Answers: 0 Comments: 1

Question Number 219724 Answers: 1 Comments: 0

prove; Π_(n=1) ^∞ (((2n+1)^3 −3(2n+1)+2)/((2n+1)^3 )) = (π/6)

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{prove}; \\ $$$$\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{3}\left(\mathrm{2}{n}+\mathrm{1}\right)+\mathrm{2}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{3}} }\:=\:\frac{\pi}{\mathrm{6}} \\ $$$$ \\ $$

Question Number 219723 Answers: 2 Comments: 0

Question Number 219722 Answers: 2 Comments: 0

Question Number 219721 Answers: 5 Comments: 0

Question Number 219710 Answers: 0 Comments: 0

∫_ρ ^( ∞) ((e^r ∙Γ(0,r))/r) dr=?? Γ(α,r)=(1/(Γ(1−α)))∙∫_0 ^( ∞) ((θ(s−1))/(s(s−1)^α ))e^(−sr) ds

$$\int_{\rho} ^{\:\infty} \:\frac{{e}^{{r}} \centerdot\Gamma\left(\mathrm{0},{r}\right)}{{r}}\:\mathrm{d}{r}=?? \\ $$$$\Gamma\left(\alpha,{r}\right)=\frac{\mathrm{1}}{\Gamma\left(\mathrm{1}−\alpha\right)}\centerdot\int_{\mathrm{0}} ^{\:\infty} \:\frac{\theta\left({s}−\mathrm{1}\right)}{{s}\left({s}−\mathrm{1}\right)^{\alpha} }{e}^{−{sr}} \mathrm{d}{s} \\ $$

Question Number 219709 Answers: 0 Comments: 0

solve Differantial Equation (y′(t))^2 =4(y(t))^3 −ay(t)−b , {a,b∈C}

$$\mathrm{solve}\:\mathrm{Differantial}\:\mathrm{Equation} \\ $$$$\left({y}'\left({t}\right)\right)^{\mathrm{2}} =\mathrm{4}\left({y}\left({t}\right)\right)^{\mathrm{3}} −{ay}\left({t}\right)−{b}\:,\:\left\{{a},{b}\in\mathbb{C}\right\} \\ $$

Question Number 219704 Answers: 2 Comments: 0

Question Number 219697 Answers: 2 Comments: 0

Question Number 219696 Answers: 2 Comments: 0

Question Number 219695 Answers: 1 Comments: 0

Question Number 219682 Answers: 0 Comments: 0

∫_0 ^( 1) ((log(1+x)∙Li_s (x))/(x∙ζ(s+1,x))) dx

$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{log}\left(\mathrm{1}+{x}\right)\centerdot\mathrm{Li}_{{s}} \left({x}\right)}{{x}\centerdot\zeta\left({s}+\mathrm{1},{x}\right)}\:{dx} \\ $$$$ \\ $$

Question Number 219678 Answers: 2 Comments: 2

Question Number 219676 Answers: 0 Comments: 0

The latex converter is not converting some symbols. Any reason why?

$$\mathrm{The}\:\mathrm{latex}\:\mathrm{converter}\:\mathrm{is}\:\mathrm{not}\:\mathrm{converting}\:\mathrm{some}\:\mathrm{symbols}.\:\mathrm{Any}\:\mathrm{reason}\:\mathrm{why}?\: \\ $$

Question Number 219668 Answers: 2 Comments: 0

Question Number 219663 Answers: 0 Comments: 0

Question Number 219662 Answers: 0 Comments: 0

Question Number 219660 Answers: 1 Comments: 0

∫_( 0) ^( 2π) (1/(a + b cos (x))) dx

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{2}\pi} \frac{\mathrm{1}}{{a}\:+\:{b}\:{cos}\:\left({x}\right)}\:{dx} \\ $$$$ \\ $$

Question Number 219659 Answers: 1 Comments: 0

prove; cos (B+C−A)−cos(C+A−B)+cos(A+B−C)−cos(A+B+C) = 4sinAcosBsinC

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{prove}; \\ $$$$\:\:{cos}\:\left({B}+{C}−{A}\right)−{cos}\left({C}+{A}−{B}\right)+{cos}\left({A}+{B}−{C}\right)−{cos}\left({A}+{B}+{C}\right)\:=\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}{sinAcosBsinC} \\ $$$$ \\ $$

Question Number 219658 Answers: 2 Comments: 0

prove Π_(n=2) ^∞ e(1−(1/n^2 ))^n^2 = (π/(e(√e)))

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{prove} \\ $$$$\:\:\:\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}\:{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\overset{{n}^{\mathrm{2}} } {\right)}=\:\frac{\pi}{{e}\sqrt{{e}}} \\ $$$$ \\ $$

Question Number 219657 Answers: 1 Comments: 0

prove; Π_(n=1) ^∞ (((5n−2)(5n−3))/((5n−1)(5n−4))) = ϕ

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{prove}; \\ $$$$\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\:\frac{\left(\mathrm{5}{n}−\mathrm{2}\right)\left(\mathrm{5}{n}−\mathrm{3}\right)}{\left(\mathrm{5}{n}−\mathrm{1}\right)\left(\mathrm{5}{n}−\mathrm{4}\right)}\:=\:\varphi \\ $$$$ \\ $$

Question Number 219651 Answers: 1 Comments: 0

Solve x^2 y^((2)) (x)+xy^((1)) (x)+(x^2 −ν^2 )y(x)=e^(−kx)

$$\mathrm{Solve} \\ $$$${x}^{\mathrm{2}} {y}^{\left(\mathrm{2}\right)} \left({x}\right)+{xy}^{\left(\mathrm{1}\right)} \left({x}\right)+\left({x}^{\mathrm{2}} −\nu^{\mathrm{2}} \right){y}\left({x}\right)={e}^{−{kx}} \\ $$

Question Number 219649 Answers: 0 Comments: 0

Solve y^((2)) (t)−t∙y(t)=0

$$\mathrm{Solve}\:{y}^{\left(\mathrm{2}\right)} \left({t}\right)−{t}\centerdot{y}\left({t}\right)=\mathrm{0} \\ $$

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