Weber Functions
Although Bessel Functions of the Second Kind are sometimes calledWeber functions, Abramowitz and Stegun (1972) define a separate Weber function as
 | (1) |
Letting 
be a Root of Unity, another set of Weber functions is defined as
 |  |  | (2) |
 | |  | (3) |
 | |  | (4) |
 | |  | (5) |
 | |  | (6) |
(Weber 1902, Atkin and Morain 1993), where
is the Dedekind Eta Function. The Weber functions satisfy the identities | |  | (7) |
 | |  | (8) |
 | |  | (9) |
 | | | (10) |
 | | | (11) |
 | | | (12) |
(Weber 1902, Atkin and Morain 1993).See also Anger Function, Bessel Function of the Second Kind, Dedekind Eta Function,j-Function, Jacobi Identities, Jacobi Triple Product, Modified StruveFunction, Q-Function, Struve Function
References
Abramowitz, M. and Stegun, C. A. (Eds.). ``Anger and Weber Functions.'' §12.3 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 498-499, 1972. Atkin, A. O. L. and Morain, F. ``Elliptic Curves and Primality Proving.'' Math. Comput. 61, 29-68, 1993. Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, pp. 68-69, 1987. Weber, H. Lehrbuch der Algebra, Vols. I-II. New York: Chelsea, pp. 113-114, 1902.
- Characteristic Factor
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