Questions on specifying order in and splicing of lists, including use of Mathematica Sequence objects.

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18
votes
0answers
306 views

Performance problems in new Sequence functions

The new-in-10.1 Sequence* family of functions should provide newly optimized methods for handling sequence problems. Happily in some cases they do! For example ...
2
votes
1answer
279 views

how can I solve integrals including recursion of some sequences of functions

I would like to solve the equations as given below in mathematica. I have written some codes before but I have no idea when there is sub indexing to indicate the series of functions. I will be very ...
4
votes
5answers
342 views

Sequence generation

If I wanted to generate a sequence that follows the pattern $$x_{n}=x_{n-1}+\dfrac{1}{2}\left(\sqrt{1-y_{n-1}\ ^{2}}-x_{n-1}\right)\\ y_{n}=y_{n-1}+\dfrac{1}{2}\left(\sqrt{1-x_{n}\ ...
7
votes
5answers
270 views

How can I tally continuous sequences in a list?

I have a stream of data like this: 0001100111100000111111001110000001111111111000000111000111110000... (I can represent them as a list, like in {0,0,0,1,1,...}, ...
10
votes
2answers
245 views

How to implement symbolic Ramanujan's summation in Mathematica?

How to implement Ramanujan's summation in symbolic form in Mathematica? For instance, I want as input the function $f(x)=x$, as output $-1/12$, as input $f(x)=1/x$, as output $\gamma$ (Euler's ...
5
votes
1answer
172 views

Find the domain in which a sequence converges

I seem to have a lot of problems in the format of: Given the sequence $a_n=\frac{n^\alpha+1}{2n^8+5}$, for $\alpha > 0$, find the values of $\alpha$ such that the sequence converges. However, ...
11
votes
4answers
763 views

How can I return a Sequence?

Recently I had the need to redefine a certain symbol in my init.m so it would be automatically omitted from any lists it appears in. I decided to redefine it to an empty sequence, e.g. ...
7
votes
1answer
175 views

How to find a recurrence relation for a sequence?

I have a sequence given by an explicit formula for n-th term: ...
2
votes
1answer
145 views

Generating a list of specific intermediate numbers associated with continued fractions

First of all, I don't know how ContinuedFraction[] or Convergents[] are implemeneted, and I think it is immaterial to my ...
1
vote
2answers
90 views

Number of sequences with a certain condition

Suppose I have the sequence {2, 4, 6, 8, 10, 12, 14, 16}. How could I calculate the number of tuples so that for every term save the first one, the difference from ...