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  • 0 posts edited
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  • 189 votes cast
Mar
18
asked Mellin transform of digamma function
Mar
17
comment First order ODE proof
oh sorry :) , no there is by definition the MOST GENERAL first order differential equation
Mar
17
comment First order ODE proof
this is just the DEFINITION of first order differntial equation in the most general case although perhaps it should be $ a(x) y' (x)+b(x)y(x)+c(x)=d(x) $ all the first order linear differential equation are of this way
Mar
16
comment $ \sum_{n=2}^\infty \frac{1}{n^3(n^3+1)}. $
use Euler Maclaurin summation formula en.wikipedia.org/wiki/Euler_Maclaurin
Mar
15
comment decimal expansion and square roots
that was the idea.. thank you
Mar
15
accepted decimal expansion and square roots
Mar
15
comment decimal expansion and square roots
um of course but assume it exists and it converges to a number of the form $ a+ \sqrt{b} $ with a and b integers, could we get a and b from its decimal expansions ?
Mar
15
asked decimal expansion and square roots
Mar
14
accepted Evaluation of a power series
Mar
13
comment Evaluation of a power series
how can in terms of hypergeometric function ? what would be the method ?? thanks
Mar
13
answered Solve $x=y\frac{dy}{dx}-\left(\frac{dy}{dx}\right)^{2}$
Mar
13
asked Evaluation of a power series
Mar
13
comment How do I find $\sum_{n=1}^\infty \frac{1}{n^n}$
in terms of integral i think i saw this sum and was equal to $$ \int_{0}^{1}dxx^{-x}= \sum_{1}^{\infty}n^{-n} $$
Mar
11
answered Contour integration using Cauchy's integral formula
Mar
10
comment Continued fractions for $\sqrt{x} $ and beyond, valid formula?
but for positive $ x >1 $ the fraction should converge since $ x-1 >0 $ will be positive :) only for divergent values or for $ x=1 $ may we have some problems.
Mar
10
accepted Continued fractions for $\sqrt{x} $ and beyond, valid formula?
Mar
10
comment Continued fractions for $\sqrt{x} $ and beyond, valid formula?
don't know but i had some similar guess which turned to be invalid :D
Mar
10
asked Continued fractions for $\sqrt{x} $ and beyond, valid formula?
Mar
10
comment How to show $\sin(-iy)=i\sinh(y)$?
use Euler's identity $ sin(x)= \frac{e^{ix}-e^{-ix}}{2i} $ and the definition of the hyperbolic sine $ sin(x)= \frac{e^{x}-e^{-x}}{2} $ now just compare :) since $ i(-i)=1 $
Mar
9
asked Padé approximant for a function $ f(x) $ always valid?