About: Bernoulli polynomials of the second kind

The Bernoulli polynomials of the second kind ψn(x), also known as the Fontana-Bessel polynomials, are the polynomials defined by the following generating function: The first five polynomials are: Some authors define these polynomials slightly differently so that and may also use a different notation for them (the most used alternative notation is bn(x)). The Bernoulli polynomials of the second kind were largely studied by the Hungarian mathematician Charles Jordan, but their history may also be traced back to the much earlier works.