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Date: 29-4-2018
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Date: 21-5-2019
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Date: 18-6-2019
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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
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(1) |
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(2) |
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(3) |
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(4) |
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(5) |
The inverse Gudermannian is implemented in the Wolfram Language as InverseGudermannian[z].
Its derivative is given by
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(6) |
It has Maclaurin series
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(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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