ANALYTIC ASPECTS OF PARTITION AND COLORED PARTITION FUNCTIONS USING q-SERIES - A.Venkatachalam; A.Gnanam (The Bioscan, 2026)
A weighted partition generating function defined by a multi-factor Euler product using analytic and computational methods. Explicit coefficient formulas are derived via convolutions of colored partition functions and Euler-type linear recurrence relations involving divisor sums are established. Asymptotic analysis shows that the coefficients exhibit exponential growth governed by dominant singularities on the boundary of the unit disk. Numerical evaluation based on truncated Euler products is investigated, and three-dimensional surface plots confirm stable convergence within the unit disk while indicating increased sensitivity near the dominant singularity. The combined results highlight the usefulness of integrating theoretical analysis with numerical computation for partition-type generating functions.