Questions tagged [continued-fractions]

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Computing continued fraction

I want to build this infinite continued fraction $$F_{n}(x)= \frac{1}{1-x\frac{(n+1)^2}{4(n+1)^2-1}F_{n+1}(x)} $$ which gives for $n=0$ $$F_{0}(x)=\dfrac{1}{1-\dfrac{(1/3)x}{1-\dfrac{(4/15)x}{1-\...
3
votes
3answers
70 views

Potential bug : missing terms in ContinuedFraction

If I use 0.23 instead of 23/100, the last continued fraction coefficient (7) is not given: ...
3
votes
0answers
43 views

ContinuedFraction: different result with different representation of argument

Why if I write: In[7]:= ContinuedFraction[3.15] FromContinuedFraction[%] N[%] I get: ...
3
votes
1answer
43 views

Unexpected behavior of ContinuedFractionK with function defined by SetDelayed

I cannot explain the following results: First, I define a function f. Then ContinuedFractionK imvolving ...
3
votes
2answers
126 views

Problems with ContinuedFractionK

I am interested in calculating the following series $$ \sum_{k=0}^{+\infty}{ \frac{ x^k }{\, a (a+1) \cdots (a+k) \,} } $$ using this continued fraction (I expect) equivalent form: $$ \cfrac{1}{a + ...
2
votes
1answer
189 views

Gauss Continued Fraction for Hypergeometric Functions

I would like to calculate the Gauss Continued Fraction for this particular Hypergeometric function: \begin{equation} _{2}F_{1}\left( 1-\frac{1}{p}, \frac{1}{p}; 1+\frac{1}{p}; x^p \right) \end{...
8
votes
1answer
196 views

Using Mathematica to find an alternative continued fraction for $\zeta(5)$

Given the Riemann zeta function $\zeta(n)$. I. $x=\zeta(3)$ Using Euler's continued fraction formula, we can form $\zeta(3)$'s cfrac as, $$Ax+B = \cfrac{1}{v_1 - \cfrac{1^6}{v_2 - \cfrac{2^6}{...