  One may consider the generalization of Jacobi polynomials and the Jacobi
function of the second kind to a general function where the index is allowed to
be a complex number instead of a non-negative integer. These functions are
referred to as Jacobi functions. In a similar fashion as associated Legendre
functions, these break into two categories, functions which are analytically
continued from the real line segment $(-1,1)$ and those continued from the real
ray $(1, \infty)$. Using properties of Gauss hypergeometric functions, we
derive multi-derivative and multi-integral representations for the Jacobi
functions of the first and second kind.
