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...

{B_{k+1+j}}{k+1+j}}={\frac {k!m!}{(k+m+1)!}}} Bernoulli polynomial Bernoulli polynomials of the second kind Bernoulli umbra Bell number Euler number Genocchi number...

Shen to study the various combinatorial properties of the cumulants. Bernoulli umbra Umbral composition of polynomial sequences Calculus of finite differences...

lion by his claw Said in 1697 by Johann Bernoulli about Isaac Newton's anonymously submitted solution to Bernoulli's challenge regarding the Brachistochrone...

Geologica Italiana, Memorie 13 (1974): 137–159. Eberli (1991) Eberli G.P., Bernoulli D., Sanders D., Vecsei A. (1993). From aggradation to progradation: the...