


Gegenbauer Functions
====================

The Gegenbauer polynomials are defined in Abramowitz & Stegun,
Chapter 22, where they are known as Ultraspherical polynomials.

.. index::
  Gegenbauer function
  Gegenbauer polynomial

.. function:: gsl_sf_gegenpoly_1(lambda, x)

.. function:: gsl_sf_gegenpoly_2(lambda, x)

.. function:: gsl_sf_gegenpoly_3(lambda, x)

 These functions evaluate the Gegenbauer polynomials :math:`C^{(\lambda)}_n(x)`
 using explicit representations for :math:`n = 1, 2, 3`.

.. function:: gsl_sf_gegenpoly_n(n, lambda, x)

 This function evaluates the Gegenbauer polynomial :math:`C^{(\lambda)}_n(x)`
 for a specific value of :math:`n`, :math:`\lambda`, :math:`x` subject to :math:`\lambda > -1/2`,
 :math:`n \geq 0`.
