Scholarlink

This chapter provides the solutions to the problems listed in Chap. 5 (Generalized Bessel functions). There are two types of problems solved in this chapter. The first type is about the properties of the generalized Mittag-Leffler and Bessel functions: \(\textrm{E}_{\alpha }(z)\) by Mittag-Leffler, \(\textrm{E}_{\alpha ,\beta }(z)\) by Wiman, \(\textrm{E}^{\gamma }_{\alpha ,\beta }(z)\) by Prabhakar, \(\textrm{E}^{\gamma ,q}_{\alpha ,\beta }(z)\) by Shukla-Prajapati, and \(\phi (\alpha ,\beta ;z)\) by Wright. The second type is about the properties of the pseudo-exponential functions. The pseudo-exponential functions are shown to be the special integrals of the elementary exponential functions. Many special integrals are shown to be simplified using the pseudo-exponential functions.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Solutions to Generalized Bessel Functions

  • 章节

  • 发表日期：

    2025年

查看全文
  • Abhishek Mishra

摘要

This chapter provides the solutions to the problems listed in Chap. 5 (Generalized Bessel functions). There are two types of problems solved in this chapter. The first type is about the properties of the generalized Mittag-Leffler and Bessel functions: \(\textrm{E}_{\alpha }(z)\) by Mittag-Leffler, \(\textrm{E}_{\alpha ,\beta }(z)\) by Wiman, \(\textrm{E}^{\gamma }_{\alpha ,\beta }(z)\) by Prabhakar, \(\textrm{E}^{\gamma ,q}_{\alpha ,\beta }(z)\) by Shukla-Prajapati, and \(\phi (\alpha ,\beta ;z)\) by Wright. The second type is about the properties of the pseudo-exponential functions. The pseudo-exponential functions are shown to be the special integrals of the elementary exponential functions. Many special integrals are shown to be simplified using the pseudo-exponential functions.