code: def _stirling_approx_tail(k):
      """Utility for `_btrs`."""
      tail_values = tf.constant(
          [
              0.0810614667953272,
              0.0413406959554092,
              0.0276779256849983,
              0.02079067210376509,
              0.0166446911898211,
              0.0138761288230707,
              0.0118967099458917,
              0.0104112652619720,
              0.00925546218271273,
              0.00833056343336287,
          ],
          dtype=k.dtype,
      )
  
      safe_tail_k = tf.clip_by_value(tf.cast(k, tf.int32), 0, 9)
      kp1sq = (k + 1) * (k + 1)
      nontail = (
          1.0 / 12 - (1.0 / 360 - 1.0 / 1260 / kp1sq) / kp1sq
      ) / (k + 1)
      return tf.where(
          k <= 9, tf.gather(tail_values, safe_tail_k), nontail
      )
  
imports: import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import sigmoid
  from tensorflow_probability.python.distributions import distribution
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import batched_rejection_sampler
  from tensorflow_probability.python.internal import distribution_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import implementation_selection
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import reparameterization
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import tensor_util
  from tensorflow_probability.python.internal import tensorshape_util
  from tensorflow_probability.python.math import special
label_desc: Use image node_id 4 for calling a global function with example usage: _stirling_approx_tail(k) and returns: tf