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  1. What is a special function? - Mathematics Stack Exchange

    In particular, elementary functions are also considered as special functions." Also, looking at the Wikipedia list (linked above) the indicator function, step functions, the absolute value function …

  2. What are special functions for? - Mathematics Stack Exchange

    If you read enough mathematics, you eventually come across several so-called "special functions". I'm always left wondering what on Earth these things are actually for. We have the …

  3. Reference Book on Special Functions - Mathematics Stack Exchange

    Jun 24, 2014 · 14 Now I'm studying the topic that uses the special functions frequently, so I find myself in need for some good reference book on the properties and equalities of the special …

  4. special functions - analytic continuation of the series $\sum_ {n=0 ...

    Nov 24, 2025 · I would like to understand how to make sense of the following divergent series, or at least to identify the appropriate analytic continuation of its general term: \begin {align} \sum_ …

  5. special functions - Analytic sum of an alternating …

    Nov 21, 2025 · Alternatively, if the sum cannot be expressed in closed form, can it be written in terms of Bessel functions or some other known special functions? Comments and suggestions …

  6. ordinary differential equations - Why Special Functions are called ...

    Jul 15, 2019 · "Special functions" are a few select functions from that set which have some sort of "interesting" properties for some or another reason and given certain names or standard …

  7. Newest 'special-functions' Questions - Mathematics Stack Exchange

    Aug 21, 2019 · This tag is for questions on special functions, useful functions that frequently appear in pure and applied mathematics (usually not including "elementary" functions).

  8. special functions - Proof of functional equation of $\psi (x)=\sum_ …

    Oct 1, 2023 · Ramanujan found a way to do this by developing his own theory of theta functions. It needs a bit of work with hypergeometric functions and may not really fit in one answer.

  9. special functions - Exponential integral representation

    Aug 18, 2015 · Explore related questions special-functions exponential-function See similar questions with these tags.

  10. special functions - Closed-form solution to the transcendental …

    Feb 28, 2023 · What do you think about generalized trigonometric hyperbolic functions that correspond to the functional equation $|y|^p−|x|^q=1$ , see the book of R. Mickens …