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Et harum scientiarum porta et clavis est Mathematica

"Mathematics is the door and key to the sciences" - Roger Bacon (~1214-1292)

$$ \sum_{n=1}^\infty\frac{1}{n^z} = \prod_{p \text{ prime}} \frac{1}{1-p^{-z}} $$


Apr
5
comment Behaviour of a function in differential equation
Is it anyhow related to Mathematica (a computer system) programming?
Jan
4
comment Solving: How to find an inverse function for this function?
Defining y[x_] := 2 + Log[Sqrt[x] - 1] you get the answer with InverseFunction[y], e.g. InverseFunction[y][2] yields 4. You don't have to care about the warning when you work with real numbers x > 1.
Oct
28
comment How to factorize an equation?
possible duplicate of Factoring polynomials to factors involving complex coefficients
Sep
18
comment Taylor series problem
@Stefano From this equation: -55.20 + 6598.80 i - 30794.40i^2 == 0. Solution i = 0.205566 is just an artefact of approximation by a Taylor series. For a bit of Mathematica code see the answer by belisarius.
Sep
18
comment Taylor series problem
@DanielLichtblau You can check these steps are correct until the last line, the result should be i == 0.00872 || i == 0.205566 it is different by a factor 10. Nevertheless approximate solution i == 0.00872 is correct, it just shouldn't be i == 0.00753.
Jun
6
comment How to plot this problem? From Greek Exams
@lafkasd If you've asked this question consider registering your account and merge it with user7851. It hasn't been obvious if this question regarded Mathematica programming or you just plotting certain mathematical object (so how to plot it ?). Therefore they have sent it here.
Jun
3
answered How to plot this problem? From Greek Exams
Jun
3
comment How to plot this problem? From Greek Exams
What do you mean by the curve v^3+a2*v^2+a1*v+a0 = 0 ? To plot all the three curves (three roots of the equation depending on a0, a1, a2)? If so then it should be a three-dimensional submanifold, not just one-parameter curve.
May
17
awarded  Constituent
May
6
awarded  Caucus
Mar
16
comment How to evaluate $I=\displaystyle\int_0^{\pi/2}x^2\ln(\sin x)\ln(\cos x)dx$
@robjohn I believe it might be proved symbolically in Mathematica. I'll check if it can be done. By the way I'm Artes not Aries.
Dec
29
awarded  Yearling
Dec
23
comment Does Pi contain all possible number combinations?
Certain practical problems related to exploring $\pi$ you may find here : mathematica.stackexchange.com/questions/6323/…
Nov
20
comment Finding the 2,147,483,647th prime number
@DanNeely In reference.wolfram.com/mathematica/tutorial/… you can find e.g. a note on Number Theoretic Functions, it says Prime and PrimePi use sparse caching and sieving. For large n, the Lagarias-Miller-Odlyzko algorithm for PrimePi is used, based on asymptotic estimates of the density of primes, and is inverted to give Prime.
Nov
19
comment Finding the 2,147,483,647th prime number
@awashburn You can compute Prime[2147483647] in Wolfram|Alpha as well, since it relies on Mathematica.
Nov
19
comment Finding the 2,147,483,647th prime number
The approximation of $\pi(x)$ is good asymptotically (prime number theorem) but for any finite number it may be far from the correct value which is 50685770143 for 2147483647 th prime. A better approximation is given by the Riemann prime counting function.
Nov
19
comment Finding the 2,147,483,647th prime number
You can compute it in Mathematica, simply Prime[2147483647] yields 50685770143. For some interesting subtleties concerning Prime I recommend reading this question : mathematica.stackexchange.com/questions/3327/…
Oct
25
comment Does Pi contain all possible number combinations?
See a related question you could find interesting : mathematica.stackexchange.com/questions/6323/…
Oct
1
awarded  Citizen Patrol
Oct
1
comment How do I account for opposite answers when calculating city block distances?
How is your question related to Mathematica programming ?