SC 740 Presentation Review

 By Deborah Dent

Fractional Bernoulli Polynomials and Application

Presented by

Suming Fang

University of Southern Mississippi

November 12, 1997

Mr. Fang presented information from an investigation conduct by Mr. Fang and Dr. Rayborn on Bernoulli numbers and polynomials. He stated that Bernoulli numbers have several orders, but he was going to concentrate on 1^st and 2^nd orders for this presentation. He first presented information on the deconvolution theorem and discussed the following applications:

• Rectangular apparatus function (Bernoulli polynomials of order one)
• Triangular apparatus function (Bernoulli polynomials of order two)
• Trapezoid apparatus function (Bernoulli polynomials with specified parameter)

Mr. Fang concluded his presentation with examples one, which were the Time-of-Flight (TOF) techniques. These techniques have been useful in the studying the velocity distribution of meta-stably excited and charged particles.