Chapter 28- Expressing a Rogers-Ramanujan q Continued Fraction in Radicals

Chapter28_6

This board is an extension of Chapter 20 on discriminants and modular functions.  It provides a method of expressing the Rogers-Ramanujan octic q continued fraction in terms of radicals. Some interesting relations of the q continued fraction with the plastic number are shown. A q modulus equation is also derived to find new radical expressions for polynomials with various complex quadratic fields. Radical form is possible if the order of the associated polynomial with discrimination (-d) is less than five or provided the real root U of f(x) is solvable by radicals. Unexpectedly the later is true for all but four of the discriminants 1 or 3 mod 4 less than 100 using a radical extension of the irreducible coefficient field.

expressing a ramanujan q continued fraction in terms of radicals_

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