# Special Functions

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## special functions

[′spesh·əl ′fəŋk·shənz]
(mathematics)
The various families of solution functions corresponding to cases of the hypergeometric equation or functions used in the equation's study, such as the gamma function.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Special Functions

in mathematics, functions belonging to various special classes that are encountered particularly often in solving problems in mathematical physics. The principal special functions are solutions of second-order linear differential equations with variable coefficients. Examples of important special functions are the hypergeometric functions, cylindrical functions, spherical functions, solid spherical harmonics, Lamé functions, and Mathieu functions. Transcendental functions that cannot be expressed in terms of elementary functions are sometimes also called special functions. Such transcendental functions include elliptic functions, the gamma function, the zeta function, the logarithmic integral, and the error function.

### REFERENCES

Smirnov, V. I. Kurs vysshei matematiki, 8th ed., vol. 3, part 2. Moscow, 1969.
Whittaker, E. T., and G. N. Watson. Kurs sovremennogo analiza, 2nd ed., part 2. Moscow, 1963. (Translated from English.)
Jahnke, E , F. Emde, and F. Lósch. Spetsial’nye funktsii: Formuly,grafiki, mblitsy, 2nd ed. Moscow, 1968. (Translated from German; contains bibliography. )
References in classic literature ?
And the art of payment has the special function of giving pay: but we do not confuse this with other arts, any more than the art of the pilot is to be confused with the art of medicine, because the health of the pilot may be improved by a sea voyage.
Special functions will be held across the country to appreciate sacrifices of police force for establishing peace.
In a statement, the IGP said besides Quran Khawani for the departed souls, special functions should be arranged at police range level in the Sindh province to appreciate sacrifices of police force for establishing peace.
Various educational institutes would arrange special functions on the vision, philosophy and poetry of Allama Mohammad Iqbal.
Special functions have been arranged at APS schools and other educational institutions to pay homage to martyrs of APS school tragedy.
Inspector general Police Punjab in this regard issued a directive to all RPOs, CPOs and DPOs to arrange special functions besides Bara Khana in their respective domains.
The reports were lodged by Zulhazmi Shariff, special functions officer to Federal Territories Minister Khalid Abdul Samad, who is also the lawyer representing the minister and Hisham Fauzi, special functions officer to Minister in the Prime Minister's Department Datuk Dr Mujahid Yusof
There Gautschi developed a number of computer algorithms for evaluating special functions, for example, for the gamma and incomplete gamma functions, and Bessel functions of the first kind.
flare TIME HM8-2U-A features 8 time ranges and 4 time and 4 special functions including stepping (inverted), watchdog and wiper interval.
Paneva-Konovska presents readers with a comprehensive examination of the use of Bessel and Mittag-Leffler functions within the fields of mathematics and the sciences through the study of enumerable families of different classes of special functions. The author covers Bessel and associated functions, generating functions of Bessel and associated Bessel functions, convergence of series in Bessel functions, and a wide variety of related subjects.
Recent advances in orthogonal polynomials, special functions, and their applications; proceedings.

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