About the Project
NIST

amplitude (am) function

AdvancedHelp

(0.004 seconds)

1—10 of 11 matching pages

1: 22.16 Related Functions
§22.16(i) Jacobi’s Amplitude ( am ) Function
Definition
Quasi-Periodicity
Integral Representation
See accompanying text
Figure 22.16.1: Jacobi’s amplitude function am ( x , k ) for 0 x 10 π and k = 0.4 , 0.7 , 0.99 , 0.999999 . … Magnify
2: 22.21 Tables
§22.21 Tables
3: 22.19 Physical Applications
§22.19(i) Classical Dynamics: The Pendulum
22.19.3 θ ( t ) = 2 am ( t E / 2 , 2 / E ) ,
See accompanying text
Figure 22.19.1: Jacobi’s amplitude function am ( x , k ) for 0 x 10 π and k = 0.5 , 0.9999 , 1.0001 , 2 . … Magnify
4: 22.1 Special Notation
The functions treated in this chapter are the three principal Jacobian elliptic functions sn ( z , k ) , cn ( z , k ) , dn ( z , k ) ; the nine subsidiary Jacobian elliptic functions cd ( z , k ) , sd ( z , k ) , nd ( z , k ) , dc ( z , k ) , nc ( z , k ) , sc ( z , k ) , ns ( z , k ) , ds ( z , k ) , cs ( z , k ) ; the amplitude function am ( x , k ) ; Jacobi’s epsilon and zeta functions ( x , k ) and Z ( x | k ) . …
5: 22.20 Methods of Computation
§22.20(vi) Related Functions
6: 19.25 Relations to Other Functions
7: Errata
  • Equation (22.19.3)
    22.19.3 θ ( t ) = 2 am ( t E / 2 , 2 / E )

    Originally the first argument to the function am was given incorrectly as t . The correct argument is t E / 2 .

    Reported 2014-03-05 by Svante Janson.

  • 8: 22.14 Integrals
    9: 29.2 Differential Equations
    29.2.5 ϕ = 1 2 π - am ( z , k ) .
    10: 29.1 Special Notation
    (For other notation see Notation for the Special Functions.) … All derivatives are denoted by differentials, not by primes. … The notation for the eigenvalues and functions is due to Erdélyi et al. (1955, §15.5.1) and that for the polynomials is due to Arscott (1964b, §9.3.2). … where ψ = am ( z , k ) ; see §22.16(i). The relation to the Lamé functions Ec ν m , Es ν m of Ince (1940b) is given by …