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The Reverend Frank Hilton Jackson (16 August 1870, Hull,
England England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe b ...
– 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''-analogue generalizations of generalized hypergeometric series, and are in turn generalized by elliptic hypergeometric series. A series ''x'n'' is called h ...
. He introduced several ''q''-analogs such as the Jackson–Bessel functions, the Jackson- Hahn-Cigler ''q''-addition, the Jackson derivative, and the
Jackson integral In q-analog theory, the Jackson integral series in the theory of special functions that expresses the operation inverse to q-differentiation. The Jackson integral was introduced by Frank Hilton Jackson. For methods of numerical evaluation, see an ...
.


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

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Selected papers

* Jackson, F. H. (1917). The q-integral analogous to Borel's integral. Messenger Math, 47, 57–64. * Jackson, F. H. (1921). Summation of q-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 q^\theta equations whose solutions are products of solutions of q^\theta equations of lower order. The Quarterly Journal of Mathematics, (1), 1-17. * Jackson, F. H. (1941). Certain q-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