Convolutions of K/(1 + χn)

Consider the probability density functions (pdfs) ƒ (χ) = K/(1 + χn for χ > 0 and n2. Pdfs of this form arise in many areas of mathematical statistics and probability theory. In this note, we derive explicit algebraic expressions for the convolutions of this pdf for n = 2, 3, 4, 5, 6. We believe that these results will be useful to theoreticians in many areas of mathematical statistics and probability theory.