The MRB constant is a mathematical constant, with decimal expansion 0.187859… (sequence A037077 in the OEIS). The constant is named after its discoverer, Marvin Ray Burns, who published his discovery of the constant in 1999. [1] Burns had initially called the constant "rc" for root constant [2] but, at Simon Plouffe's suggestion, the constant was renamed the 'Marvin Ray Burns's Constant', or "MRB constant". [3]
The MRB constant is defined as the upper limit of the partial sums [4] [5] [6] [7] [8] [9] [10]
As grows to infinity, the sums have upper and lower limit points of −0.812140… and 0.187859…, separated by an interval of length 1. The constant can also be explicitly defined by the following infinite sums: [4]
The constant relates to the divergent series:
There is no known closed-form expression of the MRB constant, [11] nor is it known whether the MRB constant is algebraic, transcendental or even irrational.
The MRB constant is a mathematical constant, with decimal expansion 0.187859… (sequence A037077 in the OEIS). The constant is named after its discoverer, Marvin Ray Burns, who published his discovery of the constant in 1999. [1] Burns had initially called the constant "rc" for root constant [2] but, at Simon Plouffe's suggestion, the constant was renamed the 'Marvin Ray Burns's Constant', or "MRB constant". [3]
The MRB constant is defined as the upper limit of the partial sums [4] [5] [6] [7] [8] [9] [10]
As grows to infinity, the sums have upper and lower limit points of −0.812140… and 0.187859…, separated by an interval of length 1. The constant can also be explicitly defined by the following infinite sums: [4]
The constant relates to the divergent series:
There is no known closed-form expression of the MRB constant, [11] nor is it known whether the MRB constant is algebraic, transcendental or even irrational.