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)
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(OEIS A091912 and A136606).
See also
Gudermannian
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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.Referenced on Wolfram|Alpha
Inverse Gudermannian
Cite this as:
Weisstein, Eric W. "Inverse Gudermannian."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InverseGudermannian.html
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