7.15.3 Can you answer these questions?

7.15.3.1 Artifacts When Plotting Results of Numerical Integration
7.15.3.2 How to solve a system with infinitely many equations?
7.15.3.3 Custom multiplication operation between variables
7.15.3.1 Artifacts When Plotting Results of Numerical Integration

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=245101

I am trying to reproduce the following graph of phase shifts as function of frequency. 
 
Please see my code bellow. I used Mathematica to solve for  t1  and ... 
[plotting] [numerical-integration]
 
asked by guestuser https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=76488 2 votes
7.15.3.2 How to solve a system with infinitely many equations?

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=245194

I need to solve the following system of (infinitely many) equations. I am looking for $V(0,0)$ 
 
$t \in \{0,1,2.....\}$ with one caveat that $s \leq 1+t$ should hold. 
 
$ s \in \{1,2,3,L-1\}$ 
 
fixed ... 
[equation-solving] [recursion]
 
asked by Monire Jalili https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=62240 1 vote
7.15.3.3 Custom multiplication operation between variables

https://mathematica.stackexchange.com/landing/r/digest?cta=question&id=245298

I am constructing polynomial expressions in the variables $s[0],s[1],...,s[n]$ and I'm trying to define a new operation to simplify the expression: 
... 
[simplifying-expressions] [polynomials] [algebraic-manipulation]
 
asked by David https://mathematica.stackexchange.com/landing/r/digest?cta=user&id=72836 1 vote