yperbolic Cosine
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
"Hyperbolic Functions." §4.5 inHandbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover
الجزء والصفحة:
...
23-11-2018
959
yperbolic Cosine
The hyperbolic cosine is defined as
 |
(1)
|
The notation 
is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). This function describes the shape of a hanging cable, known as the catenary. It is implemented in the Wolfram Language as Cosh[z].
Special values include
where 
is the golden ratio.
The derivative is given by
 |
(4)
|
where 
is the hyperbolic sine, and the indefinite integral by
 |
(5)
|
where 
is a constant of integration.
The hyperbolic cosine has Taylor series
REFERENCES:
Abramowitz, M. and Stegun, I. A. (Eds.). "Hyperbolic Functions." §4.5 inHandbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 83-86, 1972.
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, 2000.
Jeffrey, A. "Hyperbolic Identities." §2.5 in Handbook of Mathematical Formulas and Integrals, 2nd ed. Orlando, FL: Academic Press, pp. 117-122, 2000.
Sloane, N. J. A. Sequence A010050 in "The On-Line Encyclopedia of Integer Sequences."
Spanier, J. and Oldham, K. B. "The Hyperbolic Sine 
and Cosine 
Functions." Ch. 28 in An Atlas of Functions.Washington, DC: Hemisphere, pp. 263-271, 1987.
Zwillinger, D. (Ed.). "Hyperbolic Functions." §6.7 in CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, pp. 476-481 1995.
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