Cohl H.S. , COSTAS SANTOS, ROBERTO SANTIAGO
No
Arab J. Basic Appl. Sc.
Article
Científica
0.52
13/12/2023
2-s2.0-85180669855
One may consider the generalization of Jacobi polynomials and the Jacobi function of the second kind to a general function where the degree 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 (Formula presented.) and those analytically continued from the real ray (Formula presented.) Using properties of Gauss hypergeometric functions, we derive multi-derivative and multi-integral representations for the Jacobi functions of the first and second kind. © This work was authored as part of the Contributor’s official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 USC. 105, no copyright protection is available for such works under US Law.
Generalized hypergeometric functions; integral representations; Jacobi functions; Jacobi polynomials; multi-integral representations; Rodrigues-type relations