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4
votes
5answers
313 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}\ ...
2
votes
1answer
216 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 ...
11
votes
4answers
660 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
108 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
133 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
87 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 ...