FRACTIONAL BERNOULLI POLINOMIALS and APPLICATION

On last wednesday, Mr. Suming Fang gave us a presentation on Fractinal Bernoulli Polinomials and Application. Mr. Suming Fang is a graduate student of Scientific Computing, University of Southern Mississippi.

He discussed Bernoulli numbers and Bernoulli polynomials of order one and order two with shift factor, and their application. Order one Bernoulli polynomials are applied to deconvolution with rectangular apparatus function. Order two Bernoulli poly- nomials are applied to deconvolution with triangular apparatus function.

For trapezoid apparatus function, we define Bernoulli polynomials with parameter ffi. Trapezoid appara- tus function ! rectangular apparatus function, if ffi !0. Trapezoid apparatus function ! triangular apparatus function, if ffi !1, (0 Ÿ ffi Ÿ 1). It is called the Bernoulli polynomial between order one and order two with parameter ffi. 1