Bernoulli umbra
In Umbral calculus, the Bernoulli umbra B − {\displaystyle B_{-}} is an umbra, a formal symbol, defined by the relation eval B − n = B n − {\displaystyle \operatorname {eval} B_{-}^{n}=B_{n}^{-}} , where eval {\displaystyle \operatorname {eval} } is the index-lowering operator, also known as evaluation operator and B n − {\displaystyle B_{n}^{-}} are Bernoulli numbers, called moments of the umbra. A similar umbra, defined as eval B + n = B n + {\displaystyle \operatorname {eval} B_{+}^{n}=B_{n}^{+}} , where B 1 + = 1 / 2 {\displaystyle B_{1}^{+}=1/2} is also often used and sometimes called Bernoulli umbra as well.