Gudermannianadj.n.

/ɡjuːdəˈmanɪən/

Etymology: < the name of Gudermann, a German mathematician who first investigated these functions.

Mathematics.

A. adj.

Applied (by Cayley) to the function (denoted by the letters gd) defined by the equation x = log tan (¹/ ₄ π + ¹/ ₂ gd x).

ΘΚΠ

the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to functions

generating1671

exponential1704

discontinuous1803

functional1806

odd1812

periodic1820

syzygetic1850

convex1858

graphometric1865

polycyclic1869

subrational1875

synectic1876

variational1879

polyhedral1881

holomorphic1886

tropical1887

Gudermannian1888

monogeneous1888

monotonous1890

oscillating1893

monotonic1901

monotone1903

orthogonalized1909

schlicht1925

concave1942

deconvolved1974

unate1978

1888 Greenhill Chapter Integral Calculus 28 The Gudermannian function connects the circular and hyperbolic functions.

B. n.

A Gudermannian function. The circular functions of the Gudermannian of any quantity correspond to the hyperbolic functions of that quantity (e.g. tan gd x = sinh x, etc.).

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function

function1758

exponential1784

potential function1828

syzygy1850

permutant1852

Green function1863

theta-function1871

Greenian1876

Gudermannian1876

discriminoid1877

Weierstrassian function1878

gradient1887

beta function1888

distribution function1889

Riemann zeta function1899

Airy integral1903

Poisson bracket1904

Stirling approximation1908

functional1915

metric1921

Fourier transform1923

recursive function1934

utility function1934

Airy function1939

transfer function1948

objective function1949

restriction1949

multifunction1954

restriction mapping1956

scalar function1956

Langevin function1960

mass function1961

1876 A. Cayley Elem. Treat. Elliptic Functions 56 The Gudermannian.

1876 A. Cayley Elem. Treat. Elliptic Functions 56 Instead of the general function am u, we have the gudermannian gd u, giving rise to the two functions sin gd u and cos gd u, or say sg u and cg u.

This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2018).

单词	gudermannian
释义	Gudermannianadj.n. /ɡjuːdəˈmanɪən/ Etymology: < the name of Gudermann, a German mathematician who first investigated these functions. Mathematics. A. adj. Applied (by Cayley) to the function (denoted by the letters gd) defined by the equation x = log tan (¹/ ₄ π + ¹/ ₂ gd x). ΘΚΠ the world > relative properties > number > algebra > [adjective] > relating to expressions > relating to functions generating1671 exponential1704 discontinuous1803 functional1806 odd1812 periodic1820 syzygetic1850 convex1858 graphometric1865 polycyclic1869 subrational1875 synectic1876 variational1879 polyhedral1881 holomorphic1886 tropical1887 Gudermannian1888 monogeneous1888 monotonous1890 oscillating1893 monotonic1901 monotone1903 orthogonalized1909 schlicht1925 concave1942 deconvolved1974 unate1978 1888 Greenhill Chapter Integral Calculus 28 The Gudermannian function connects the circular and hyperbolic functions. B. n. A Gudermannian function. The circular functions of the Gudermannian of any quantity correspond to the hyperbolic functions of that quantity (e.g. tan gd x = sinh x, etc.). ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function function1758 exponential1784 potential function1828 syzygy1850 permutant1852 Green function1863 theta-function1871 Greenian1876 Gudermannian1876 discriminoid1877 Weierstrassian function1878 gradient1887 beta function1888 distribution function1889 Riemann zeta function1899 Airy integral1903 Poisson bracket1904 Stirling approximation1908 functional1915 metric1921 Fourier transform1923 recursive function1934 utility function1934 Airy function1939 transfer function1948 objective function1949 restriction1949 multifunction1954 restriction mapping1956 scalar function1956 Langevin function1960 mass function1961 1876 A. Cayley Elem. Treat. Elliptic Functions 56 The Gudermannian. 1876 A. Cayley Elem. Treat. Elliptic Functions 56 Instead of the general function am u, we have the gudermannian gd u, giving rise to the two functions sin gd u and cos gd u, or say sg u and cg u. This entry has not yet been fully updated (first published 1900; most recently modified version published online June 2018). < adj.n.1876
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