Crank-Nicolson, finite difference method, time fracional-order Black-Scholes model, numerical simulation, multi-dimensional models

Abstract

Three classes of infinite series containing binomial coefficient $ \binom{3n}{n} $, harmonic-like numbers, and an independent variable "$ y $" are examined. Several algebraic formulae in closed form are established, including, as special cases, three conjectured values for numerical series by Z.-W. Sun. This is fulfilled by integrating Lambert's series and manipulating the cubic transformations for the $ _3{F_2} $-series through the "coefficient extraction" method.

Keywords

• lambert's series
• harmonic number
• binomial coefficient
• dilogarithm function
• bailey's cubic transformation