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)
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