A RAMANUJAN-TYPE SERIES FOR 1/π WITH EXPONENTIAL AND RADICAL TERMS AND ULTRA-FAST CONVERGENCE

We construct a new Ramanujan-type series for 1/π associated with the order of conductor $163$ in the imaginary quadratic field Q(√-3).The series simultaneously involves the constants e (Euler's number) and √3, while its coefficients are explicit algebraic numbers of degree $54$ and colossal size.Every additional term yields approximately $385$ correct decimal digits of 1/π, a convergence speed that dramatically surpasses all previously known series of the same family, including the celebrated Chudnovsky series.All statements are proved in full detail. {equation}{eq:main_abstract}{\,1/π\;=\;∑ₙ₌₀∞{({13}_n)\,({23}_n)\,({12})_n}{(n!)^3}\,(A₁₆₃\,n+B₁₆₃)\,(-e-163π√3)ⁿ.\,}{equation}The algebraic integers A₁₆₃,B₁₆₃ are given in the Main Theorem and Appendix.