On Generalized Exponential Integrals and Related Functions.
JOHNS HOPKINS UNIV BALTIMORE MD
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The so called exponential function YSup mSub n x is governed by an m1nth order homogeneous differential equation and includes the generalized exponential integrals Esup msub n x and their related functions Fsup msub n x. In the present paper, recursion formulas and differential relations similar to those for the generalized exponential integrals are imposed on the YSup msub n x. As a result, the multiplicity of arbitrary constants independent of n. Furthermore, the form of the related functions is such that it suggests comparison with the series expansions of the generalized exponential integrals. This comparison leads to expressions for the arbitrary constants in terms of Riemann Zeta functions involving only even values of the argument. Finally, the series expansion for the generalized exponential integral of order m is shown to be equal to the related function of order m1 plus a rapidly convergent power series in the independent variable x. Author
- Numerical Mathematics