# am function

(0.002 seconds)

## 1—10 of 29 matching pages

##### 3: 22.19 Physical Applications
###### §22.19(i) Classical Dynamics: The Pendulum
22.19.3 $\theta(t)=2\operatorname{am}\left(t\sqrt{E/2},\sqrt{2/E}\right),$
##### 4: 22.1 Special Notation
The functions treated in this chapter are the three principal Jacobian elliptic functions $\operatorname{sn}\left(z,k\right)$, $\operatorname{cn}\left(z,k\right)$, $\operatorname{dn}\left(z,k\right)$; the nine subsidiary Jacobian elliptic functions $\operatorname{cd}\left(z,k\right)$, $\operatorname{sd}\left(z,k\right)$, $\operatorname{nd}\left(z,k\right)$, $\operatorname{dc}\left(z,k\right)$, $\operatorname{nc}\left(z,k\right)$, $\operatorname{sc}\left(z,k\right)$, $\operatorname{ns}\left(z,k\right)$, $\operatorname{ds}\left(z,k\right)$, $\operatorname{cs}\left(z,k\right)$; the amplitude function $\operatorname{am}\left(x,k\right)$; Jacobi’s epsilon and zeta functions $\mathcal{E}\left(x,k\right)$ and $\mathrm{Z}\left(x|k\right)$. …
##### 6: 19.25 Relations to Other Functions
19.25.30 $\operatorname{am}\left(u,k\right)=R_{C}\left({\operatorname{cs}}^{2}\left(u,k% \right),{\operatorname{ns}}^{2}\left(u,k\right)\right),$
##### 7: William P. Reinhardt
Older work on the scattering theory of the atomic Coulomb problem led to the discovery of new classes of orthogonal polynomials relating to the spectral theory of Schrödinger operators, and new uses of old ones: this work was strongly motivated by his original ownership of a 1964 hard copy printing of the original AMS 55 NBS Handbook of Mathematical Functions. …
##### 8: Errata
• Equation (22.19.3)
22.19.3 $\theta(t)=2\operatorname{am}\left(t\sqrt{E/2},\sqrt{2/E}\right)$

Originally the first argument to the function $\operatorname{am}$ was given incorrectly as $t$. The correct argument is $t\,\sqrt{E/2}$.

Reported 2014-03-05 by Svante Janson.

• ##### 9: Mathematical Introduction
The NIST Handbook has essentially the same objective as the Handbook of Mathematical Functions that was issued in 1964 by the National Bureau of Standards as Number 55 in the NBS Applied Mathematics Series (AMS). … As a consequence, in addition to providing more information about the special functions that were covered in AMS 55, the NIST Handbook includes several special functions that have appeared in the interim in applied mathematics, the physical sciences, and engineering, as well as in other areas. …
##### 10: 8.21 Generalized Sine and Cosine Integrals
8.21.18 $f(a,z)=\operatorname{si}\left(a,z\right)\cos z-\operatorname{ci}\left(a,z% \right)\sin z,$
8.21.19 $g(a,z)=\operatorname{si}\left(a,z\right)\sin z+\operatorname{ci}\left(a,z% \right)\cos z.$