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;; Psi (digamma) functions
;; Liam Healy, Mon May 1 2006 - 22:11
;; Time-stamp: <2011-01-10 10:21:07EST psi.lisp>
;; Copyright 2006, 2007, 2008, 2009, 2011 Liam M. Healy
;; Distributed under the terms of the GNU General Public License
;;
;; This program is free software: you can redistribute it and/or modify
;; it under the terms of the GNU General Public License as published by
;; the Free Software Foundation, either version 3 of the License, or
;; (at your option) any later version.
;;
;; This program is distributed in the hope that it will be useful,
;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
;; GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License
;; along with this program. If not, see <http://www.gnu.org/licenses/>.
(in-package :gsl)
;;; antik:psi means "pounds per square inch" but there's no conflict
;;; here with the function #'gsl:psi, so we shadow import the symbol
;;; from antik.
(shadowing-import 'antik:psi)
;;;;****************************************************************************
;;;; Digamma Function
;;;;****************************************************************************
(defgeneric psi (x)
(:documentation "The psi, or digamma, function."))
(defmfun psi ((n integer))
"gsl_sf_psi_int_e" ((n :int) (ret sf-result))
:definition :method
:documentation ; FDL
"Domain: n integer, n > 0.")
(defmfun psi ((x float))
"gsl_sf_psi_e" ((x :double) (ret sf-result))
:definition :method
:documentation ; FDL
"Domain: x /= 0.0, -1.0, -2.0, ...")
(defmfun psi-1+iy (x)
"gsl_sf_psi_1piy_e" ((x :double) (ret sf-result))
:documentation ; FDL
"The real part of the digamma function
on the line 1+i y, Re[psi(1 + i y)].")
;;;;****************************************************************************
;;;; Trigamma Function
;;;;****************************************************************************
(export 'psi-1)
(defgeneric psi-1 (x)
(:documentation "The Trigamma function."))
(defmfun psi-1 ((n integer))
"gsl_sf_psi_1_int_e" ((n :int) (ret sf-result))
:definition :method
:documentation ; FDL
"Domain: n integer, n > 0.")
(defmfun psi-1 ((x float))
"gsl_sf_psi_1_e" ((x :double) (ret sf-result))
:definition :method
:documentation ; FDL
"Domain: x /= 0.0, -1.0, -2.0, ...")
;;;;****************************************************************************
;;;; Polygamma
;;;;****************************************************************************
(defmfun psi-n (m x)
"gsl_sf_psi_n_e" ((m :int) (x :double) (ret sf-result))
:documentation ; FDL
"The polygamma function psi^{(m)}(x)} for m >= 0, x > 0.")
;;;;****************************************************************************
;;;; Examples and unit test
;;;;****************************************************************************
(psi 4)
(psi 4.0d0)
(psi-1+iy 2.0d0)
(psi-1 4)
(psi-1 4.0d0)
(psi-n 2 4.0d0))