A formula for pi involving nested radicals

作者：Abrarov S M^*; Quine B M

来源：Ramanujan Journal, 2018, 46(3): 657-665.

DOI：10.1007/s11139-018-9996-8

• Constant pi
• Arctangent function
• Nested radical

We present a new formula for pi involving nested radicals with rapid convergence. This formula is based on the arctangent function identity with argument , whereis a nested radical consisting of k square roots. The computational test we performed reveals that the proposed formula for pi provides a significant improvement in accuracy as the integer k increases.

• 出版日期2018-8