Dick said:I can't evaluate it but I can look it up. It's BesselI(0,2)/BesselI(1,2). The inverse of Sloane A052119. http://www.research.att.com/~njas/sequences/A052119
A "Nasty Continued Fraction" is a type of mathematical expression that involves a never-ending sequence of fractions. It is typically denoted by the symbol [a0; a1, a2, a3, ...], where the a's are coefficients or constants. This type of fraction is considered "nasty" because it can be difficult to simplify or calculate.
The main difference between a "Nasty Continued Fraction" and a regular continued fraction is that a "Nasty Continued Fraction" has coefficients that are not necessarily integers. This makes it more complex and challenging to work with, as it requires more advanced mathematical techniques to manipulate and solve.
"Nasty Continued Fractions" have many applications in fields such as finance, physics, and computer science. They are used to approximate irrational numbers, model physical systems, and improve the efficiency of algorithms. For example, the Golden Ratio, which is often found in nature and used in art and design, can be expressed as a "Nasty Continued Fraction".
There are various methods for simplifying or evaluating a "Nasty Continued Fraction". One approach is to use continued fraction arithmetic, which involves manipulating the fractions in a specific way to get a more manageable expression. Another method is to convert the "Nasty Continued Fraction" into a regular continued fraction, which may be easier to work with. Additionally, there are computer algorithms that can approximate the value of a "Nasty Continued Fraction" to a desired degree of accuracy.
Yes, there are several well-known "Nasty Continued Fractions" that have been studied extensively by mathematicians. One example is the continued fraction for Euler's number, e = [2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, ...]. Another famous example is the continued fraction for the square root of 2, √2 = [1; 2, 2, 2, 2, ...]. These fractions have interesting properties and have been used in many mathematical proofs and applications.