/**
 * Jacobi elliptic functions sn, cn, dn.
 *
 * Uses the parameter convention `m = k^2` (matching scipy's
 * `scipy.special.ellipj(u, m)` and mpmath's `ellipfun(..., u, m)`), not the
 * modulus-angle convention some texts use.
 *
 * Computed via the descending Landen transformation / arithmetic-geometric
 * mean (AGM) method (Abramowitz & Stegun 16.4, the Bulirsch algorithm):
 * build the AGM sequences
 *
 *   a_0 = 1, b_0 = sqrt(1 - m), c_0 = sqrt(m)
 *   a_{i+1} = (a_i + b_i) / 2
 *   b_{i+1} = sqrt(a_i * b_i)
 *   c_{i+1} = (a_i - b_i) / 2
 *
 * until c_N is negligible, then descend the amplitude
 *
 *   phi_N = 2^N * a_N * u
 *   phi_{i-1} = (phi_i + asin((c_i / a_i) * sin(phi_i))) / 2   for i = N..1
 *
 * so that sn(u,m) = sin(phi_0), cn(u,m) = cos(phi_0),
 * dn(u,m) = sqrt(1 - m * sn^2(u,m)).
 *
 * @packageDocumentation
 */
/**
 * Jacobi elliptic function sn(u, m), parameter convention m = k^2.
 *
 * @param u - Argument
 * @param m - Parameter m = k^2, must be in [0, 1]
 * @returns sn(u, m)
 *
 * @example
 * jacobiSN(0.5, 0.3) // ~0.4742156227
 */
export declare function jacobiSN(u: number, m: number): number;
/**
 * Jacobi elliptic function cn(u, m), parameter convention m = k^2.
 *
 * @param u - Argument
 * @param m - Parameter m = k^2, must be in [0, 1]
 * @returns cn(u, m)
 *
 * @example
 * jacobiCN(0.5, 0.3) // ~0.8804087364
 */
export declare function jacobiCN(u: number, m: number): number;
/**
 * Jacobi elliptic function dn(u, m), parameter convention m = k^2.
 *
 * @param u - Argument
 * @param m - Parameter m = k^2, must be in [0, 1]
 * @returns dn(u, m)
 *
 * @example
 * jacobiDN(0.5, 0.3) // ~0.9656789647
 */
export declare function jacobiDN(u: number, m: number): number;
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