Henry E. Fettis

James C. Caslin

The Jacobian elliptic functions sn(w) cn(w) dn(w) are tabulated to five decimals in the complex w = u + iv plane as functions of the nome q = .005(.005).4 for u/K = 0(.1)1. and v/K' = 0(.1)1. where q = e to the minus (pi K'/K) power and K and K' are complete elliptic integrals with moduli k and k' = square root of (l-sq. k), respectively.

Elliptic Functions for Complex Arguments

Aerospace Research Laboratories (U.S.)

The report contains 15 place tables of the modified Bessel functions I(sub 0(x), I(sub 1(x), e (sup -x) I(sub o)(x), e(sup -X) I(sub 1(x) for x=0(0.001)10.

Table of Modified Bessel Functions

A Table of the Complete Elliptic Integral of the First Kind for Complex Values of the Modulus

Ten Place Tables of the Jacobian Elliptic Functions

The report contains ten place tables of the Jacobian elliptic functions am(u, k) sn(n, k) cn(u, k) dn(u, k), E(am(u, k)) where u = the integral from zero to phi of (d(theta)/the square root of (1-(k squared)(sin squared theta))); am(u, k) = phi; sn(u, k) = sin phi; cn(u, k) = cos phi; dn(u, k) = the square root of (1 - (k squared)(sin squared phi)); E(phi, k) = the integral from zero to phi of the square root of (1 - (k squared)(sin squared theta))d(theta) for k squared = .950 (.001).999, u = 0(.01)K(k) where K(k) = the integral from zero to pi/2 of (d(theta)/the square root of (1 - (k squared)(sin squared theta))).

Ten Place Tables of the Jacobian Elliptic Functions: ARL71-0081

Let z = sn(w, k) be the Jacobian sine-amplitude function. The tables list five-D values of the quantity w = u + iv where z is given by z = a + ib, for some given values. The values of u and v are expressed as decimal portions of the quarter-period K and K' respectively.

James C. Caslin

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