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This chapter explores some more interesting properties of the pseudo-exponential functions. First, it is proved that the pseudo-exponential functions are expressible as a finite-polynomial combination of each other. Next, the differential equations satisfied by the pseudo-exponential functions are derived. Finally, the star product of the series is defined, and also its integral representation is derived. In the problems listed in this chapter, several interesting series are summed using the special integral of a problem in Chap. 5. Special integrals and series sums are derived using the star product identity.

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Series Sums Using Special Integrals

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  • 发表日期：

    2025年

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  • Abhishek Mishra

摘要

This chapter explores some more interesting properties of the pseudo-exponential functions. First, it is proved that the pseudo-exponential functions are expressible as a finite-polynomial combination of each other. Next, the differential equations satisfied by the pseudo-exponential functions are derived. Finally, the star product of the series is defined, and also its integral representation is derived. In the problems listed in this chapter, several interesting series are summed using the special integral of a problem in Chap. 5. Special integrals and series sums are derived using the star product identity.