root/trunk/special-functions/debye.lisp

;; Deybe functions
;; Liam Healy, Sun Mar 19 2006 - 14:34
;; Time-stamp: <2008-02-16 20:07:26EST debye.lisp>
;; $Id$

#|
;;; FDL
The Debye functions D_n(x) are defined by the following integral,
D_n(x) = n/x^n \int_0^x dt (t^n/(e^t - 1))
For further information see Abramowitz &
Stegun, Section 27.1.
|#

(in-package :gsl)

(defmfun debye-1 (x)
  "gsl_sf_debye_1_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The first-order Debye function D_1(x) = (1/x) \int_0^x dt (t/(e^t - 1)).")

(defmfun debye-2 (x)
  "gsl_sf_debye_2_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The second-order Debye function
   D_2(x) = (2/x^2) \int_0^x dt (t^2/(e^t - 1)).")

(defmfun debye-3 (x)
  "gsl_sf_debye_3_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The third-order Debye function
   D_3(x) = (3/x^3) \int_0^x dt (t^3/(e^t - 1)).")

(defmfun debye-4 (x)
  "gsl_sf_debye_4_e" ((x :double) (ret sf-result))
  :documentation                        ; FDL
  "The fourth-order Debye function
  D_4(x) = (4/x^4) \int_0^x dt (t^4/(e^t - 1)).")

#|
(make-tests debye
  (debye-1 1.0d0)
  (debye-2 1.0d0)
  (debye-3 1.0d0)
  (debye-4 1.0d0))
|#

(LISP-UNIT:DEFINE-TEST DEBYE
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.7775046341122482d0 4.117962028082377d-16)
   (MULTIPLE-VALUE-LIST (DEBYE-1 1.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.7078784756278294d0 4.948781517277596d-16)
   (MULTIPLE-VALUE-LIST (DEBYE-2 1.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.6744155640778147d0 5.450931753448871d-16)
   (MULTIPLE-VALUE-LIST (DEBYE-3 1.0d0)))
  (LISP-UNIT::ASSERT-NUMERICAL-EQUAL
   (LIST 0.654874068886737d0 5.769372522202218d-16)
   (MULTIPLE-VALUE-LIST (DEBYE-4 1.0d0))))