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seen Jul 16 at 1:15

Jul
1
awarded  Critic
Jul
1
answered Continuous function proof by definition
Jul
1
comment Continuous function proof by definition
and what if you are asked to show that the square root function is continuous at the point $c=0$ ? then both answers provided here are wrong. that is, $\delta_1 = \epsilon \sqrt{c}$, $\delta_2 = \min \lbrace c, \epsilon \sqrt{c} \rbrace$ and $\delta_3 = \epsilon / \sqrt{c}$ will not work for $c = 0$, we have $\delta_1$ and $\delta_2$ to not only prove nothing, but they are less than useless choices: they say nothing about continuity, and $\delta_3$ is an awful choice as you are in the bizarre world that your restriction is infinite. there is no such thing as infinite restriction. down-voted
May
22
awarded  Yearling
Jan
10
comment Rational roots of polynomials
What if we we had $(x-a_1)(x-a_2)...$ with $a_i$ to be distinct and rational for all $i=1,2,...$. then for any natural number $n$, pick $n$ distinct numbers $\lbrace a_1, \ldots, a_n \rbrace$ and just consider the polynomial $\Pi_{i=1}^{n} (x-a_i)$. ??
Dec
18
comment Calculate the following integral $\int_0^{\pi/2} \frac{\sin^m x\,\mathrm{d}x}{\sin x + \cos x}$, $m=2k-1$
I had a similar idea, here are some more values of $a$ and $b$. $(a_{11},b_{11}) = (73/512, 2/15)$, $(a_{13},b_{13})=(523/4096,13/120)$, $(a_{15},b_{15})= (119/1024, 151/1680)$.
Dec
8
answered Real Analysis and Statistics
Aug
13
awarded  Yearling
Jun
16
comment Black-Scholes PDE to heat equation, nonconstant coefficients
What are you specifically looking for? My solution gives a good platform to show you how to solve your problem. Perhaps you are looking for a shorter solution? Or?
Jun
12
revised Black-Scholes PDE to heat equation, nonconstant coefficients
added 4 characters in body
Jun
12
answered Black-Scholes PDE to heat equation, nonconstant coefficients
Jun
12
comment Black-Scholes PDE to heat equation, nonconstant coefficients
First it is suggested that you understand how the constant coefficient Black Scholes partial differential equation transforms to the heat equations. Then the non-constant coefficient case is easy to understand. Never the less, here are some links: Transforming the BS-pde into the heat equation if $r = r(t)$ and $\sigma = \sigma (t)$ : [LINK][1] (page 24) But this does not give you the answer that you exactly seek. I will provide a solution later. [1]: staff.city.ac.uk/bogdan.stefanski.1/FDE2.pdf
Jun
12
comment Suggestions for using a new text about a topic on which someone already possess a first course or advanced idea
Definitions are the essential item in mathematics. The understanding, introduction, explanation and placement of definitions is of higher importance than proving theorems. It is relatively easy to follow a theorem or "see" a proposition. But it is the definition that gives it purpose: that launchs it. Your post is excellent but can be expanded.
Jun
9
revised Markov Chain Converging in Single Step
added 412 characters in body
Jun
9
answered Markov Chain Converging in Single Step
Jun
9
awarded  Commentator
Jun
9
comment Meaning of $\alpha$ in Laguerre polynomials
You may see $\alpha$ as a parameter that can change a number of things: the asymptotic distribution and such. The [Wikipedia article][1] gives many results: some on the distribution and some on the derivatives of the polynomials depending on the value of $\alpha$ (whether it is integer or $0$). I am sure if you dig deep enough you can find a more satisfying answer, the generalised Laguerre polynomials and related polynomials/transforms have a lot of coefficients as these are the coefficients in specific DE's that are used to define them. [1]: en.wikipedia.org/wiki/Laguerre_polynomials
Apr
7
comment 1+2+3+4+… = -1/12
Thank you Zev! I tried to search but nothing came up. My question is answered.
Apr
7
asked 1+2+3+4+… = -1/12
Mar
27
comment Equivalent definition of Riemann integrals
Specifically this is the proof that a Darboux integral is equivalent to a Riemann integral (if they exist).