///|
let k1_arrA : ReadOnlyArray[Double] = [
  -7.02386347938628759343E-18, -2.42744985051936593393E-15, -6.66690169419932900609E-13,
  -1.41148839263352776110E-10, -2.21338763073472585583E-8, -2.43340614156596823496E-6,
  -1.73028895751305206302E-4, -6.97572385963986435018E-3, -1.22611180822657148235E-1,
  -3.53155960776544875667E-1, 1.52530022733894777053E0,
]

///|
let k1_arrB : ReadOnlyArray[Double] = [
  -5.75674448366501715755E-18, 1.79405087314755922667E-17, -5.68946255844285935196E-17,
  1.83809354436663880070E-16, -6.05704724837331885336E-16, 2.03870316562433424052E-15,
  -7.01983709041831346144E-15, 2.47715442448130437068E-14, -8.97670518232499435011E-14,
  3.34841966607842919884E-13, -1.28917396095102890680E-12, 5.13963967348173025100E-12,
  -2.12996783842756842877E-11, 9.21831518760500529508E-11, -4.19035475934189648750E-10,
  2.01504975519703286596E-9, -1.03457624656780970260E-8, 5.74108412545004946722E-8,
  -3.50196060308781257119E-7, 2.40648494783721712015E-6, -1.93619797416608296024E-5,
  1.95215518471351631108E-4, -2.85781685962277938680E-3, 1.03923736576817238437E-1,
  2.72062619048444266945E0,
]

///|
/// Computes the modified Bessel function of the third kind of order one of the argument.
pub fn bessel_k1(x : Double) -> Double {
  let z = 0.5 * x
  if z <= 0.0 {
    return @double.infinity
  }
  if x <= 2.0 {
    let y = x * x - 2.0
    let y = log(z) * bessel_i1(x) + chbevl(y, k1_arrA) / x
    return y
  }
  return exp(-x) * chbevl(8.0 / x - 2.0, k1_arrB) / sqrt(x)
}

///|
/// `k1` is an alias for `bessel_k1`.
pub let k1 : (Double) -> Double = bessel_k1