7.18.2 Greatest hits from previous weeks

7.18.2.1 Multivariable Taylor expansion does not work as expected

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=15023

The basic multivariable Taylor expansion formula around a point is as follows: 
 
$$ 
f(\mathbf r + \mathbf a) = f(\mathbf r) + (\mathbf a \cdot \nabla )f(\mathbf r) + \frac{1}{2!}(\mathbf a \cdot \nabla)... 
[calculus-and-analysis] [series-expansion]
 

asked by matheorem https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=4742 65 votes

answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 73 votes

7.18.2.2 How to calculate contour integrals with Mathematica?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=34073

How to calculate the integral of $\frac{1}{\sqrt{4 z^2 + 4 z + 3}}$ over the unit circle counterclockwise for each branch of the integrand? 
[calculus-and-analysis] [complex]
 

asked by user64494 https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=7152 42 votes

answered by Artes https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=184 64 votes

7.18.2.3 What does "Tag Integer is Protected" message mean?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=6738

(Newbie question) 
 
For every function I define I get this message: 
When I close and reopen Mathematica, and re-enter the function definition, I don't get the message anymore. What does it mean? 
[warning-messages]
 

asked by stevenvh https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1450 11 votes

answered by J. M.'s ennui https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=50 13 votes

7.18.2.4 Is there an open source implementation of Mathematica-the-language?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=4454

I've seen questions before such as "What is the best open-source equivalent for Mathematica?", but that specific question (and that line of inquiry in general) cares more about the computer algebra ... 
[programming] [open-source]
 

asked by sblom https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=178 124 votes

answered by Simon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=34 86 votes

7.18.2.5 How to express trigonometric equation in terms of of given trigonometric function?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=434

How can I express a trigonometric equation / identity in terms of a given trigonometric function? 
 
using following trigonometric identities 
 
... 
[functions] [trigonometry]
 

asked by Prashant Bhate https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=99 30 votes

answered by Simon https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=34 37 votes

7.18.2.6 How can I plot a graph of an integral?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=78451

I want to plot the following function: 
 
$$\int \left(\frac{\Gamma (x+1)}{2}-\frac{\Gamma (x-1)}{2}\right) \, dx$$ 
[plotting]
 

asked by Anixx https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=651 4 votes

answered by k_v https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=24727 9 votes

7.18.2.7 Find eigen energies of time-independent Schrödinger equation

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=32293

I'm trying to get the eigenvalues of a one dimensional time-independent Schrödinger equation, 
 
$-\frac{h^2}{2m_0}\frac{d^2\psi}{dx^2}+U(x)~\psi=Ei~\psi$ 
 
where U(x) is some potential and Ei is the ... 
[equation-solving] [physics] [parametric-functions]
 

asked by xslittlegrass https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=1364 49 votes

answered by Jens https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=245 46 votes