Linked Questions

5
votes
2answers
245 views

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 ...
1
vote
2answers
233 views

Function to Represent Recursive Integral

I'd like to represent the following recursive integral equation to evaluate/graph (for $n\leq3$): $$K_{i,n}\left(x\right)=\int_{x}^{\infty}K_{i,n-1}\left(y\right)dy$$ where $$K_{i,0}\left(x\right)=...
0
votes
2answers
217 views

Super recursive function

I have read about how to define a recursive function using RecurrenceTable but for $u(100)$ you need all 99 previous terms. The posts doesn't help me. I want to ...
9
votes
1answer
1k views

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 ...
3
votes
1answer
209 views

Recursion with substitution mathematica

When writing out some mathematical equation like we see on the picture here I got the problem of writing out all terms. I know what recursion means and have done recursion for example for the ...
2
votes
1answer
55 views

Functions that remember some arguments while not remembering other arguments

I would like to some programming that is very generic. Particularly I am interested in the following: Let's say I want to write a function ...
2
votes
1answer
149 views

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: ...
0
votes
1answer
61 views

Memoization (or otherwise) for a recurrent definition of a (double) sequence of functions

Beside I've found answers to similar questions (e.g. this), I can't adapt them to my case. I am interested in the following sequence of functions $p_{m,n}(t)$, where $m$ and $n$ are integer: $$ \...
0
votes
1answer
79 views

Create recursive sequence of functions with memoization

I am trying to create a sequence of functions and have it properly memoize the results. The recursive operation is simply convolution, so it possible there is a better way to do this (obviously, if I ...
0
votes
1answer
111 views

Nested integration

I wish to perform the following nested integral: \begin{align} I_n=\int_{-\infty}^\infty dx_n~f(x_n,x_{n+1})\int_{-\infty}^\infty dx_{n-1}~f(x_{n-1},x_n)...\int_{-\infty}^\infty dx_1~f(x_1,x_2)\int_{-\...
0
votes
1answer
411 views

Tabulating Numeric Approximation

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)...
39
votes
0answers
2k views

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 ...
0
votes
0answers
76 views

Dummy variable in nested integral operator

I am trying to make a nested integral operator where the output function of one step must be applied to the dummy variable to be integrated in the next step. Here my code: ...
0
votes
0answers
70 views

Reuse symbolic polynomial

Suppose I have a function that returns a polynomial in x, GetPoly[params_,x_]:=GetPoly[params,x]... but it is quite slow, so ...
0
votes
0answers
42 views

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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