F. H. Jackson

The Reverend Frank Hilton Jackson (16 August 1870, Hull, England – 27 April 1960) was an English clergyman and mathematician who worked on basic hypergeometric series. He introduced several q-analogs such as the Jackson–Bessel functions, the Jackson-Hahn-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

• Chaundy, T. W. (1962), "Frank Hilton Jackson", J. London Math. Soc., 37: 126–128, doi:10.1112/jlms/s1-37.1.126

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.