The MRB constant is a

mathematical constant A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. Cons ...

, with decimal expansion . The constant is named after its discoverer, Marvin Ray Burns, who published his discovery of the constant in 1999. Burns had initially called the constant "rc" for root constant but, at Simon Plouffe's suggestion, the constant was renamed the 'Marvin Ray Burns's Constant', or "MRB constant". The MRB constant is defined as the

upper limit In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (that is, eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion for a function (see limit of a function). For a ...

of the partial sums :

s_n = \sum_^n (-1)^k k^

n

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: :

0.187859\ldots = \sum_^ (-1)^k (k^ - 1) = \sum_^ \left((2k)^ - (2k-1)^\right).

The constant relates to the divergent series: :

\sum_^ (-1)^k k^.

There is no known closed-form expression of the MRB constant, nor is it known whether the MRB constant is algebraic,

transcendental Transcendence, transcendent, or transcendental may refer to: Mathematics * Transcendental number, a number that is not the root of any polynomial with rational coefficients * Algebraic element or transcendental element, an element of a field exten ...

or even irrational.

References

External links

{{Portal, Mathematics
Official site of M.R. Burns, constant's namesake and discoverer
Mathematical constants