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### Memoization of a function defined by a recurrence relation [duplicate]

I have a function which is defined by the following recurrence relation $$h_{n}(x)=h_{n-1}(x)+\frac{\mathrm{e}^{-x^2}}{2^n n!}H_{n}(x)H_{n-1}(x)$$ with the initial condition $h_{0}(x)=0$ and where the ...
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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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### 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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### Performance tuning in Mathematica?

What performance tuning tricks do you use to make a Mathematica application faster? MATLAB has an amazing profiler, but from what I can tell, Mathematica has no similar functionality.
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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 ...
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### Why does Expand not work within a function?

I'm writing this fairly simple function: ...
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### 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 ...
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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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### 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 ...
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### 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:  \...
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### 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 ...
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### 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_{-\...
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### 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 ...