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### Numerical evaluation of ChebyshevT

When I evaluate the following Chebyshev series of the first kind in two different ways, I get two very different results: ...
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### Dynamic Programming with delayed evaluation

By using dynamical programming, we can save intermediate steps for recursive relations, as in f[n_]:= f[n] = f[n-1] + f[n-2] However, this only stores ...
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### Keeping memory to reduce the running time of recursion [duplicate]

I am using the following recursion in Mathematica to compute W[n, 1, s] for given n and s: ...
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### List of Tribonacci Polynomials with Mathematica? [duplicate]

I want to list top ten of Tribonacci polynomials. I have following algorithm, but it doesnt work. ...
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### Can one identify the design patterns of Mathematica?

... or are they unnecessary in such a high-level language? I've been thinking about programming style, coding standards and the like quite a bit lately, the result of my current work on a mixed .Net/...
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### Only perform a symbolic differentiation once

I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form ...
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### Compiling a recursive formula

My question is related to computing what is called "invariant measure" for a particular well known fractal - the Sierpinski triangle. We have an array m of four two by two matrices, say ...
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### Fast Spherical Harmonics radiative transfer

This is a rather specific question and I apologize for spamming you with some lengthy code. But it could be interesting for some reader and maybe you can help out, so please bear with me. I am using ...
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### How to generate a recurrent sequence

How to generate this type of sequence? $$f(n, x) = x f'(n-1, x) \hspace{2 mm}, f(0, x) = e^x$$ How do I evaluate it for numerical values for $x = 1$ or any number?
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### Why does Mathematica use [[ ]] notation for array indexing?

I am confused by why Mathematica uses [[3]] to get the 3rd element, or [[i,j] to get the i,j-th element of a 2D array. This ...
414 views

I was wondering how to approximate or tabulate values for this numeric approximation: It is the following: The confusing part is how to implement the subscripts in mathematica. $y_{i+1} = (t_i - y_i)... 2answers 1k views ### Why does Expand not work within a function? I'm writing this fairly simple function: ... 3answers 1k views ### recursive integration I am trying to do multiple integrations recursively. For instance, I would like to do the following equation for arbitrary integer$n$:$\displaystyle R_n(t) = \int_0^t \mathrm dt' R_0(t-t') R_{n-1}(...
Let $f_{0}(x):[0,1]\to[0,1]$ be defined by f_{0}(x):=\begin{cases} 3x, & \text{if } x\in [0,\frac{1}{3}] \\ \\ -3x+2, & \text{if } x\in (\frac{1}{3}, \frac{2}{3}] \\ \\ 3x+2, & \...