Blogs about: Continued Fractions
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Hypergeometric formulas for Ramanujan’s continued fractions 2
(continued from yesterday’s post) III. Icosahedral group Given the Rogers-Ramanujan identities (see also here), I observed that, where, as in the previous post, is the j-function, , , and . Sin… more →
tpiezas
Continued Fractions
wrote 3 months ago: … more →
Srinivasa Ramanujan @ 125
wrote 5 months ago: Design: RK | Click on the image to enlarge … more →
structure and uncertainty, Bristol, Sept. 27
wrote 7 months ago: The last sessions at the SuSTain workshop. were equally riveting but I alas had to leave early to ge … more →
Moments, Hankel determinants, orthogonal polynomials, Motzkin paths, and continued fractions
wrote 8 months ago: Previously we described all finite-dimensional random algebras with faithful states. In this post we … more →
Little Mathematics Library - Fascinating Fractions
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wrote 8 months ago: The theory of continued fractions is vast. This booklet covers only its fundamentals, but it contain … more →
Hypergeometric formulas for Ramanujan's continued fractions 2
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wrote 10 months ago: (continued from yesterday’s post) III. Icosahedral group Given the Rogers-Ramanujan identities … more →
Hypergeometric formulas for Ramanujan's continued fractions 1
wrote 10 months ago: There are five Platonic solids, two are duals to another two, while the tetrahedron is self-dual. As … more →
Ramanujan's continued fraction for Catalan's constant
wrote 1 year ago: Ramanujan was a goldmine when it came to continued fractions (and many others). In this post, two f … more →
Zudilin's continued fraction for Zeta(4)
wrote 1 year ago: Euler proved the following general continued fraction formula, which automatically gives a represent … more →
The silver ratio and a continued fraction for log(2)
wrote 1 year ago: Define the three sequences, The last two are Apery numbers and have been discussed previously. The f … more →
A new continued fraction for Zeta(3)?
wrote 1 year ago: Continuing the discussion from the previous post, Ramanujan also gave a continued fraction for as, w … more →
Continued fractions for Zeta(2) and Zeta(3)
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wrote 1 year ago: It seems there is a nice “pattern” between the continued fractions for the Riemann zeta … more →
Some of Ramanujan's continued fractions for pi
wrote 1 year ago: The digits of pi go on forever apparently with no discernible pattern. However, there are beautifull … more →
The Brioschi quintic and the Rogers-Ramanujan continued fraction
wrote 1 year ago: Given Ramanujan’s constant, where , why do we know, in advance, that the quintic, is solvable … more →
Percentages for sceptics: part III
wrote 1 year ago: I wanted to do some self-criticism of my previous two posts in this series: You can calculate the mi … more →
Leap
wrote 1 year ago: Seems a good day to point out this old article I wrote, in which I show that if, instead of skipping … more →
SPCS 7
wrote 1 year ago: Today we will make some preparations towards the application of Avila-Viana simplicity criterion to … more →
Continued fractions, Bohr sets, and the Littlewood conjecture
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wrote 1 year ago: Let be an element of the unit circle, let , and let . We define the (rank one) Bohr set to be the se … more →
Évariste Galois in the métro...
wrote 1 year ago: This morning, while waiting for a very late métro, I took those pictures from the platform. These po … more →
