mathjs/src/function/trigonometry/acoth.js

'use strict'

const deepMap = require('../../utils/collection/deepMap')

function factory (type, config, load, typed) {
  /**
   * Calculate the hyperbolic arccotangent of a value,
   * defined as `acoth(x) = atanh(1/x) = (ln((x+1)/x) + ln(x/(x-1))) / 2`.
   *
   * For matrices, the function is evaluated element wise.
   *
   * Syntax:
   *
   *    math.acoth(x)
   *
   * Examples:
   *
   *    math.acoth(0.5)       // returns 0.8047189562170503
   *
   * See also:
   *
   *    acsch, asech
   *
   * @param {number | Complex | Array | Matrix} x  Function input
   * @return {number | Complex | Array | Matrix} Hyperbolic arccotangent of x
   */
  const acoth = typed('acoth', {
    'number': function (x) {
      if (x >= 1 || x <= -1 || config.predictable) {
        return isFinite(x) ? (Math.log((x + 1) / x) + Math.log(x / (x - 1))) / 2 : 0
      }
      return new type.Complex(x, 0).acoth()
    },

    'Complex': function (x) {
      return x.acoth()
    },

    'BigNumber': function (x) {
      return new type.BigNumber(1).div(x).atanh()
    },

    'Array | Matrix': function (x) {
      return deepMap(x, acoth)
    }
  })

  acoth.toTex = { 1: `\\coth^{-1}\\left(\${args[0]}\\right)` }

  return acoth
}

exports.name = 'acoth'
exports.factory = factory