Commonly Used Special Functions: Definitions and Computing

Dingyü Xue () and Lu Bai ()
Additional contact information
Dingyü Xue: Northeastern University
Lu Bai: Shenyang University, School of Information Engineering

Chapter 2 in Fractional Calculus, 2024, pp 19-56 from Springer

Abstract: Abstract Special functions are dedicated mathematical functions invented by mathematicians. For instance, if the integrand is $$f(x)=\textrm{e}^{-x^2}$$ f ( x ) = e - x 2 , the analytical solution to its indefinite integralsIndefinite integral does not exist. Therefore, mathematicians invented a special function $$\textrm{erf}(x)$$ erf ( x ) to express the integral expression. This special function is regarded as the analytical solution of the integral problem. In different applications, many other such special functions are invented. For instance, Gamma function and Beta function and so on. Many special functions are invented for indefinite integral and differential equation problems.

Date: 2024
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-99-2070-9_2

Ordering information: This item can be ordered from
http://www.springer.com/9789819920709

DOI: 10.1007/978-981-99-2070-9_2

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().