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Τι (ποιος) είναι Naperian logarithm - ορισμός

MATHEMATICAL FUNCTION

Napier's logarithm; Naperian logarithm; Naperian system of logarithms

Napierian logarithm

[ne?'p??r??n]

¦ noun another term for natural logarithm.

Origin

C19: named after the Scottish mathematician John Napier (1550-1617).

Napierian logarithm

The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this natural logarithmic function, although it is named after him.

https://en.wikipedia.org/wiki/Napierian_logarithm

natural logarithm

LOGARITHM TO THE BASE OF THE MATHEMATICAL CONSTANT E

Natural logarithm integral condition; Integrating the derivative of the logarithm of a function; Natural log; Natural logarithms; ㏑; Base-e logarithm; Ln(x); Ln x; Log natural; Base e; Natural Log; Natural Logarithm; Hyperbolic logarithms; Logarithmus naturalis; Base e logarithm; Logarithm of the base e; Natural logarithm plus 1; Natural logarithm plus 1 function; Lnp1; Ln1p; Ln+1; Logh (mathematics); Logh (function); Log1p; Log1p(x); Lnp1(x); Ln1p(x); LN1+X; LN(1+X); Ln(1+x); Natural system of logarithms; Natural logarithm near one; Natural logarithm plus one; Natural logarithm plus one function; Natural logarithm near 1; Ln(1 + x); Ln(x + 1); Ln(x+1)

¦ noun Mathematics a logarithm to the base e (2.71828 ...).

Βικιπαίδεια

Napierian logarithm

The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this natural logarithmic function, although it is named after him. However, if it is taken to mean the "logarithms" as originally produced by Napier, it is a function given by (in terms of the modern natural logarithm):

\mathrm {NapLog} (x)=-10^{7}\ln(x/10^{7})

The Napierian logarithm satisfies identities quite similar to the modern logarithm, such as

\mathrm {NapLog} (xy)\approx \mathrm {NapLog} (x)+\mathrm {NapLog} (y)-161180956

or

\mathrm {NapLog} (xy/10^{7})=\mathrm {NapLog} (x)+\mathrm {NapLog} (y)

In Napier's 1614 Mirifici Logarithmorum Canonis Descriptio, he provides tables of logarithms of sines for 0 to 90°, where the values given (columns 3 and 5) are

\mathrm {NapLog} (\theta )=-10^{7}\ln(\sin(\theta ))

https://en.wikipedia.org/wiki/Napierian logarithm