On Certain Appell Polynomials and Their Generalizations Based on the Tsallis q -Exponential

The integrals ∫ x^n e^-x dx , ∫ x^n e^x dx , ∫ x^n sinhx dx , and ∫ x^n sinx dx are seen to give rise to sets of Appell polynomials with the exponential generating functions e^xt/(1 - t) , e^xt/(1 + t) , e^xt/( 1 - t^2 ) , and e^xt/( 1 + t^2 ) , respectively, and these are special cases of sets of Appell polynomials with the generating functions e^xt/( 1 ± t^m ) . Generalizations of these polynomials arising from the replacement of e^xt by the Tsallis q -exponential are studied.