Artifact 663821d053d0149715840128400e8f56e9f0b5b658ea8e535c6e4727e2800b87:
- File
r35/xlog/specfmor.log
— part of check-in
[f2fda60abd]
at
2011-09-02 18:13:33
on branch master
— Some historical releases purely for archival purposes
git-svn-id: https://svn.code.sf.net/p/reduce-algebra/code/trunk/historical@1375 2bfe0521-f11c-4a00-b80e-6202646ff360 (user: arthurcnorman@users.sourceforge.net, size: 4452) [annotate] [blame] [check-ins using] [more...]
Codemist Standard Lisp 3.54 for DEC Alpha: May 23 1994 Dump file created: Mon May 23 10:39:11 1994 REDUCE 3.5, 15-Oct-93 ... Memory allocation: 6023424 bytes +++ About to read file ndotest.red % % More Tests for REDUCE Special Functions Package % % Winfried Neun, ZIB Berlin, February 1993 % load_package specfn; (specfn) % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 1. Binomial Coefficients and Stirling numbers % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Binomial (2,1/2); 16 ------ 3*pi on rounded; Binomial (2.1,2); 1.155 off rounded; Binomial (n,2); gamma(n + 1) ---------------- 2*gamma(n - 1) 1/Binomial (49,6); 1 ---------- 13983816 % for those who play Lotto in Germany. Stirling1(10,5); -269325 Stirling2(10,5); 42525 % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 2. Bernoulli Polynomials % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= BernoulliP (4,x); 4 3 2 30*x - 60*x + 30*x - 1 --------------------------- 30 BernoulliP (4,1/2); 7 ----- 240 % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 4. Laguerre Polynomials % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= LaguerreP(3,x); 3 2 - x + 9*x - 18*x + 6 ------------------------- 6 LaguerreP(2,1,x); 2 x - 6*x + 6 -------------- 2 % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 5. Legendre and Jacobi Polynomials % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= LegendreP (2,x); 2 3*x - 1 ---------- 2 LegendreP (3,x); 2 x*(5*x - 3) -------------- 2 LegendreP (6,3,x); 2 4 2 315*sqrt( - x + 1)*x*(11*x - 14*x + 3) ------------------------------------------- 2 JacobiP (2,1,3/4,x); 2 437*x + 38*x - 91 -------------------- 128 % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 6. Chebychev Polynomials % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= ChebyshevT(2,x); 2 2*x - 1 ChebyshevT(3,x); 2 x*(4*x - 3) ChebyshevU(2,x); 2 4*x - 1 ChebyshevU(3,x); 2 4*x*(2*x - 1) % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 7. Hermite Polynomials % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= HermiteP (2,x); 2 2*(2*x - 1) HermiteP (3,x); 2 4*x*(2*x - 3) % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 8. Gegenbauer Polynomials % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= GegenbauerP(2,5,x); 2 5*(12*x - 1) GegenbauerP(3,2,x); 2 4*x*(8*x - 3) % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 9. Some well-known Infinite Sums % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= off exp; sum(1/m^4,m,1,infinity); 4 pi ----- 90 sum((-1)^m/m^4,m,1,infinity); 4 7*pi ------- 720 sum(1/(2*m-1)^4,m,1,infinity); 4 pi ----- 96 sum((-1)^m/(2*m-1)^3,m,1,infinity); 3 pi ----- 32 on exp; sum((-1)^m/(2*m-1)^2,m,1,infinity); catalan % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 10. Euler Numbers and Polynomials % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= Euler(6); -61 EulerP(4,x); 3 2 x*(x - 2*x + 1) EulerP(4,1/2); 5 ---- 16 % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 11. Integral Functions % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= on rounded; Shi(3.4); 6.50998313882 Si(3.4); 1.84191398333 Chi(3.4); *** ROUNDBF turned on to increase accuracy 6.50209216532 Ci(3.4); - 0.00451807793074 Ei(Pi); 10.9283743893 erfc(2.0); 0.00467773498105 Fresnel_C(3.1); 0.561593902462 Fresnel_S(3.1); 0.581815868171 off rounded; df(Si(z),z); sin(z) -------- z limit(Si(x),x,infinity); pi ---- 2 limit(Fresnel_S(x),x,infinity); 1 --- 2 s_i(x); 2*si(x) - pi -------------- 2 defint(cos(t)/t,t,X,INFINITY); - ci(x) % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= % 12. Misc Functions % =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= defint(log(t)/(1-t),t,1,x); dilog(x) on rounded; dilog(3.1); - 1.49114561815 off rounded; end; (TIME: specfmor 4034 4234) End of Lisp run after 4.08+1.58 seconds