Taylor Series Expressions
It is possible to express the above functions as Taylor series:
The function sinh x has a Taylor series expression with only odd exponents for x. Thus it is an odd function, that is, −sinh x = sinh(−x), and sinh 0 = 0.
The function cosh x has a Taylor series expression with only even exponents for x. Thus it is an even function, that is, symmetric with respect to the y-axis. The sum of the sinh and cosh series is the infinite series expression of the exponential function.
where
- is the nth Bernoulli number
- is the nth Euler number
Read more about this topic: Hyperbolic Function
Famous quotes containing the words taylor, series and/or expressions:
“All we can get out of a Shaw play is two hours and a half of mental exhilaration. We are, inscrutably, denied the pleasure of wondering what Shaw means, or whether he is sincere.”
—Bert Leston Taylor (18661921)
“Every man sees in his relatives, and especially in his cousins, a series of grotesque caricatures of himself.”
—H.L. (Henry Lewis)
“Preschoolers think and talk in concrete, literal terms. When they hear a phrase such as losing your temper, they may wonder where the lost temper can be found. Other expressions they may hear in times of crisisraising your voice, crying your eyes out, going to pieces, falling apart, picking on each other, you follow in your fathers footstepsmay be perplexing.”
—Ruth Formanek (20th century)