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One of the trigonometric functions:

another notation is . Its domain of definition is the whole real line apart from the points


The secant is an unbounded even -periodic function. The derivative of the secant is

The indefinite integral of the secant is

The secant can be expanded in a series:


The series expansion is valid in the domain of definition of , i.e. not for the points (*).


[a1] K. Knopp, "Theorie und Anwendung der unendlichen Reihen" , Springer (1964) (English translation: Blackie, 1951 & Dover, reprint, 1990)
[a2] M. Abramowitz, I.A. Stegun, "Handbook of mathematical functions" , Dover, reprint (1965) pp. §4.3
How to Cite This Entry:
Secant. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by Yu.A. Gor'kov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article