Continued fractions and expansions of reals

Continued fractions, Farey sequences, Stern–Brocot tree, Engel, Pierce, Lüroth and similar series expansions of real numbers.

Part 1 of 2

• Continued fractions of alternating series
• Continued fractions of Laurent series
• Continued fractions of quadratic irrationals
• Engel expansions
• Extended continuants and bi-infinite continued fractions
• Farey fractions with a given numerator
• Farey sequences
• Farey staircase
• Folding lemma and paperfolding continued fractions
• Gauss–Kuzmin masses of continued fraction strings
• Gauss–Kuzmin–Wirsing operator
• Hata's Farey formula for Euler's constant
• Lüroth series
• Periodic continued fractions
• Mallows representation of irrational numbers
• Pierce expansions
• Polynomial continued fractions and Farey paths
• TRIP-Stern sequences
• Laplace Q-polynomial families
• Solutions of \(P u^2 + Q u y + R y^2 = 1\) give convergents of \(-Q/(2P)\)

Part 2 of 2

• Strict growth of continued-fraction denominators

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