restart;f := proc ( x , i ) local j, fn, fn1, fn2; if i = 0 then return x; elif i = 1 then return x/2; end if; fn1 := x/2; fn2 := x; for j from 2 to i do fn := 3*fn1+1/2*fn2; fn2 := fn1; fn1 := fn; end do; end proc:evalf(f(7,17));

NiMkIis2cyssViEiIg==

f := proc ( x , i ) if i = 0 then return x; elif i = 1 then return x/2; else return 3*f(x,i-1)+1/2*f(x,i-2); end if; end proc:evalf(f(7,17));

NiMkIis2cyssViEiIg==

restart;fib := proc ( i ) local j, fn, fn1, fn2; if i = 1 then return 1; elif i = 2 then return 1; end if; fn1 := 1; fn2 := 1; for j from 3 to i do fn := fn1 + fn2; fn2 := fn1; fn1 := fn; end do; end proc:fib(23);

NiMiJmQnRw==

fib(29);

NiMiJ0hVXg==

fib := proc ( i ) if i = 1 then return 1; elif i = 2 then return 1; else return fib(i-1) + fib(i-2); end if; end proc:

restart;hilb := proc ( f , gr, min , max ) local m1, i, j, a1, l1, k, m2, i2, j2, a2, l2, k2, h, g, res, loes, grad; with(LinearAlgebra): grad := gr+1; m2 := Matrix(grad); for i2 from 1 to grad do for j2 from 1 to grad do m2[i2,j2] := Int((x^(j2+i2-2)),x=min..max); end do; end do; a2 := Vector(grad,symbol=a); l2 := Matrix(grad,1); for k2 from 1 to grad do l2[k2,1] := Int(f(x)*x^(k2-1),x=min..max); end do; print(m2.a2=l2); m1 := Matrix(grad); for i from 1 to grad do for j from 1 to grad do m1[i,j] := int((x^(j+i-2)),x=min..max); end do; end do; a1 := Vector(grad,symbol=a); l1 := Vector(grad); for k from 1 to grad do l1[k] := int(f(x)*x^(k-1),x=min..max); end do; print(m1.a1=l1); for i from 1 to grad do h := 0; for j from 1 to grad do h := h + a[j]*m1[i,j]; end do; g[i] := h = l1[i]; print(g[i]); end do; res:=solve({seq(g[i],i=1..grad)},{seq(a[i],i=1..grad)}); loes := 0; for i from 1 to grad do loes := loes + a[i]*x^(i-1); end do; printf("\n\t\t\t\t\t\t\tDie Loesung lautet:\n"); print(eval(evalf(loes),evalf(res))); return (eval(loes,res)); end proc:g := unapply(hilb(x->x*ln(x), 3, 1, 4),x);

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NiMvLComSSJhRzYiNiMiIiIiI0AmRiY2IyIiIyMiJGIjIiIlJkYmNiMiIiQjIiVCNSIiJiZGJjYjRjAjIiVsOEYtLCYtSSNsbkc2JEkqcHJvdGVjdGVkR0Y/SShfc3lzbGliR0YnRiwiJEciIyEkYiMiIztGKQ==NiMvLComSSJhRzYiNiMiIiIjIiRiIyIiJSZGJjYjIiIjIyIlQjUiIiYmRiY2IyIiJCMiJWw4Ri8mRiY2I0YsIyImJFE7IiIoLCYtSSNsbkc2JEkqcHJvdGVjdGVkR0ZBSShfc3lzbGliR0YnRi4jIiVbP0YyIyElQjUiI0RGKQ== Die Loesung lautet: NiMsKiQhKWRcc3EhIikiIiJJInhHNiIkIikoWzkoR0YmKiRGKCIiIyQiKUV3MVdGJiokRigiIiQkISlTMF9JISIqNiM+SSJnRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCwtSSNsbkc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiMiIiMjIidXaDsiJSg9IyMhJi4qUSIkSCgiIiIqJiwmRi0jISYnSHJGOSMiJ2AzTCIlZ1tGOkY6OSRGOkY6KiYsJkYtIyImUyVIRjkjISUmcCciJFYjRjpGOkZCRjNGOiomLCZGLSMhJis3IkY2IyIlSl4iJWU5RjpGOkZCIiIkRjpGJUYlRiU=

with(stats):

Warning, these names have been redefined: anova, describe, fit, importdata, random, statevalf, statplots, transform

xp := [1.0,2.0,3.0,4.0];

NiM+SSN4cEc2IjcmJCIjNSEiIiQiIz9GKSQiI0lGKSQiI1NGKQ==

fp := map(x->x*ln(x),xp);

NiM+SSNmcEc2IjcmJCIiIUYoJCIraFZIJ1EiISIqJCIrbm8kZUgkRiskIitXdTxYYkYr

ff := fit[leastsquare[[x,y], y=a1*x^3+a2*x^2+a3*x+a4, {a1,a2,a3,a4}]]([xp,fp]);

NiM+SSNmZkc2Ii9JInlHRiUsKiokSSJ4R0YlIiIkJCEraEJdZEkhIzYqJEYqIiIjJCIrTEJ1XVchIzVGKiQiK3AhbzRsI0YzJCErJDNnZnonRjMiIiI=

f :=unapply(rhs(ff), x);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCoqJDkkIiIkJCEraEJdZEkhIzYqJEYuIiIjJCIrTEJ1XVchIzVGLiQiK3AhbzRsI0Y3JCErJDNnZnonRjciIiJGJUYlRiU=

#ef := sum((f(op(i,xp))-op(i,fp))^2,i=1..nops(xp));

f(x);

NiMsKiokSSJ4RzYiIiIkJCEraEJdZEkhIzYqJEYlIiIjJCIrTEJ1XVchIzVGJSQiK3AhbzRsI0YvJCErJDNnZnonRi8iIiI=

g(x);

NiMsLC1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IyIiIyMiJ1doOyIlKD0jIyEmLipRIiRIKCIiIiomLCZGJCMhJidIckYxIyInYDNMIiVnW0YyRjJJInhHRilGMkYyKiYsJkYkIyImUyVIRjEjISUmcCciJFYjRjJGMkY6RitGMiomLCZGJCMhJis3IkYuIyIlSl4iJWU5RjJGMkY6IiIkRjI=

plot({abs(x*ln(x)-g(x)),abs(x*ln(x)-f(x))},x=1..4);

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

restart;tschebyschew := proc ( i , min , max ) return seq(1/2*((max-min)*cos((2*k-1)/(2*i)*Pi)+min+max),k=1..i); end proc:lagrange := proc( liste1 , liste2) local res, zaehler, nenner, laenge, i, n; Digits:=20; res := 0; if nops(liste1) = nops(liste2) then laenge := nops(liste1); for n from 1 to laenge do zaehler := 1; nenner := 1; for i from 1 to laenge do if i <> n then zaehler := zaehler * (x - op(i,liste1)); nenner := nenner * (op(n,liste1)-op(i,liste1)); end if; end do; res := res + ((zaehler/nenner)*op(n,liste2)); end do; else printf("Die Listen sind nicht gleich lang"); end if; res := sort(expand(res)); return res; end proc:

l1 := [1.0,2.0,3.0,4.0];

NiM+SSNsMUc2IjcmJCIjNSEiIiQiIz9GKSQiI0lGKSQiI1NGKQ==

l2 := map(x->x*ln(x),l1);

NiM+SSNsMkc2IjcmJCIiIUYoJCIraFZIJ1EiISIqJCIrbm8kZUgkRiskIitXdTxYYkYr

fa:=lagrange(l1,l2);

NiM+SSNmYUc2IiwqKiRJInhHRiUiIiQkITNMTExMTDddZEkhIz4qJEYoIiIjJCIzKysrK2w5dV1XISM9RigkIjNNTExMeSsoNGwjRjEkITQsKysrK1VoZnonRiwiIiI=

l1 := [tschebyschew(4,1,4)];

NiM+SSNsMUc2IjcmLCYtSSRjb3NHNiRJKnByb3RlY3RlZEdGK0koX3N5c2xpYkdGJTYjLCRJI1BpR0YrIyIiIiIiKSMiIiQiIiMjIiImRjVGMSwmLUYpNiMsJEYvI0Y0RjJGM0Y2RjEsJkY5IyEiJEY1RjZGMSwmRihGPkY2RjE=

l2 := map(x->x*ln(x),l1);

NiM+SSNsMkc2IjcmKiYsJi1JJGNvc0c2JEkqcHJvdGVjdGVkR0YsSShfc3lzbGliR0YlNiMsJEkjUGlHRiwjIiIiIiIpIyIiJCIiIyMiIiZGNkYyRjItSSNsbkdGKzYjRihGMiomLCYtRio2IywkRjAjRjVGM0Y0RjdGMkYyLUY6NiNGPUYyKiYsJkY+IyEiJEY2RjdGMkYyLUY6NiNGRUYyKiYsJkYpRkZGN0YyRjItRjo2I0ZLRjI=

fb:=sort(evalf(lagrange(l1,l2)));

NiM+SSNmYkc2IiwqKiRJInhHRiUiIiQkISp1W3crJCEjNSokRigiIiMkIipualJSJSEiKkYoJCIraS5DVUdGLCQhKVR5K3EhIikiIiI=

plot({abs(x*ln(x)-fa),abs(x*ln(x)-fb)},x=1..4);

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