Inverse Gudermannian
المؤلف:
Beyer, W. H.
المصدر:
"Gudermannian Function." CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press
الجزء والصفحة:
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10-10-2019
1498
Inverse Gudermannian
The inverse function of the Gudermannian 
gives the vertical position 
in the Mercator projection in terms of the latitude 
and may be defined for 
by
The inverse Gudermannian is implemented in the Wolfram Language as InverseGudermannian[z].
Its derivative is given by
 |
(6)
|
It has Maclaurin series
 |
(7)
|
(OEIS A091912 and A136606).
REFERENCES:
Beyer, W. H. "Gudermannian Function." CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 164, 1987.
Sloane, N. J. A. Sequences A091912 and A136606 in "The On-Line Encyclopedia of Integer Sequences."
Zwillinger, D. (Ed.). "Gudermannian Function." §6.9 in CRC Standard Mathematical Tables and Formulae, 31st ed. Boca Raton, FL: CRC Press, pp. 530-532, 1995.
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