The Reverend Frank Hilton Jackson (16 August 1870,
Hull
Hull may refer to:
Structures
* The hull of an armored fighting vehicle, housing the chassis
* Fuselage, of an aircraft
* Hull (botany), the outer covering of seeds
* Hull (watercraft), the body or frame of a sea-going craft
* Submarine hull
Ma ...
,
England
England is a Countries of the United Kingdom, country that is part of the United Kingdom. It is located on the island of Great Britain, of which it covers about 62%, and List of islands of England, more than 100 smaller adjacent islands. It ...
– 27 April 1960) was an English clergyman and mathematician who worked on
basic hypergeometric series
In mathematics, basic hypergeometric series, or ''q''-hypergeometric series, are q-analog, ''q''-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series.
A series ''x'n'' is ...
. He introduced several
''q''-analogs such as the
Jackson–Bessel functions, the Jackson-
Hahn
Hahn may refer to:
Places
*Hahn (crater), on the Moon
*Hahn (Holzhausen), a hill in Hesse, Germany
*Hahn, Rhineland-Palatinate, a municipality in Germany
**Hahn Air Base, a former frontline NATO facility near Hahn
**Frankfurt–Hahn Airport
* Ha ...
-Cigler ''q''-addition, the
Jackson derivative, and the
Jackson integral.
Further reading
*Ernst, T. (2012). A Comprehensive Treatment of q-Calculus. Springer Science & Business Media.
*Gasper, G., Rahman, M.(2004). Basic Hypergeometric Series. Cambridge University Press.
References
*
Selected papers
* Jackson, F. H. (1917). The
-integral analogous to Borel's integral. Messenger Math, 47, 57–64.
* Jackson, F. H. (1921). Summation of
-hypergeometric series. Messenger of Math, 57, 101–112.
* Jackson, F. H. (1928). Examples of a generalization of Euler's transformation for power series. Messenger Math, 57, 169–187.
* Jackson, F. H. (1940). The
equations whose solutions are products of solutions of
equations of lower order. The Quarterly Journal of Mathematics, (1), 1-17.
* Jackson, F. H. (1941). Certain
-identities. The Quarterly Journal of Mathematics, (1), 167–172.
* Jackson, F. H. (1942). On basic double hypergeometric functions. The Quarterly Journal of Mathematics, (1), 69–82.
* Jackson, F. H. (1944). Basic double hypergeometric functions (II). The Quarterly Journal of Mathematics, (1), 49–61.
1870 births
1960 deaths
English mathematicians
Q-analogs
Special functions
{{UK-mathematician-stub