# Wichtungsfaktoren
> H[i]:=Int(l[i](x),x=-1..1);
> 

                                  1
                                 /
                                |
                       H[i] :=  |   l[i](x) dx
                                |
                               /
                                 -1

# n=5
> a:=sqrt(245-14*sqrt(70))/21; b:=sqrt(245+14*sqrt(70))/21;

                                        1/2 1/2
                            (245 - 14 70   )
                       a := -------------------
                                    21


                                        1/2 1/2
                            (245 + 14 70   )
                       b := -------------------
                                    21

> l[1]:=(x+a)*(x-0)*(x-a)*(x-b)/((-b+a)*(-b-0)*(-b-a)*(-b-b)):
> L[1]:=subs(x=-b,%):
> l[2]:=(x+b)*(x-0)*(x-a)*(x-b)/((-a+b)*(-a-0)*(-a-a)*(-a-b)):
> L[2]:=subs(x=-a,%):
> l[3]:=(x+b)*(x+a)*(x-a)*(x-b)/((0+b)*(0+a)*(0-a)*(0-b)):
> L[3]:=subs(x=0,%):
> l[4]:=(x+b)*(x+a)*(x-0)*(x-b)/((a+b)*(a+a)*(a-0)*(a-b)):
> L[4]:=subs(x=a,%):
> l[5]:=(x+b)*(x+a)*(x-0)*(x-a)/((b+b)*(b+a)*(b-0)*(b-a)):
> L[5]:=subs(x=b,%):
> Digits:=15:
> H[1]:=evalf(int(l[1],x=-1..1)); H[2]:=evalf(int(l[2],x=-1..1));
>  H[3]:=evalf(int(l[3],x=-1..1)); H[4]:=evalf(int(l[4],x=-1..1));
>  H[5]:=evalf(int(l[5],x=-1..1));
> 

                      H[1] := 0.236926885056187


                       H[2] := 0.47862867049938


                       H[3] := 0.56888888888889


                       H[4] := 0.47862867049937


                      H[5] := 0.236926885056185

# Aufgrund der Symmetrie zu x = 0 stimmen die Wichtungsfaktoren
# paarweise berein, so dass
#  man beispielsweise fr n = 10 nur 5 Wichtungsfaktoren ermitteln muss.
# Zu beachten ist,
# dass bei ungeraden n die Sttzstelle x = 0 bercksichtigt werden muss.
# 
# n = 10
> A:=0.148874338981631: B:=0.433395394129247:
> C:=0.679409568299024: d:=0.865063366688985:
> E:=0.973906528517172:
> l[6]:=(x+A)*(x+B)*(x+C)*(x+d)*(x+E)*(x-B)*(x-C)*(x-d)*(x-E)/
> ((A+A)*(A+B)*(A+C)*(A+d)*(A+E)*(A-B)*(A-C)*(A-d)*(A-E)):
> L[6]:=subs(x=A,%):
> l[7]:=(x^2-A^2)*(x^2-C^2)*(x^2-d^2)*(x^2-E^2)*(x+B)/
> ((B+B)*(B^2-A^2)*(B^2-C^2)*(B^2-d^2)*(B^2-E^2)):
> L[7]:=subs(x=B,%):
> l[8]:=(x+C)*(x^2-A^2)*(x^2-B^2)*(x^2-d^2)*(x^2-E^2)/
> ((C+C)*(C^2-A^2)*(C^2-B^2)*(C^2-d^2)*(C^2-E^2)):
> L[8]:=subs(x=C,%):
> l[9]:=(x+d)*(x^2-A^2)*(x^2-B^2)*(x^2-C^2)*(x^2-E^2)/
> ((d+d)*(d^2-A^2)*(d^2-B^2)*(d^2-C^2)*(d^2-E^2)):
> L[9]:=subs(x=d,%):
> l[10]:=(x+E)*(x^2-A^2)*(x^2-B^2)*(x^2-C^2)*(x^2-d^2)/
> ((E+E)*(E^2-A^2)*(E^2-B^2)*(E^2-C^2)*(E^2-d^2)):
> L[10]:=subs(x=E,%):
> H[6]:=int(l[6],x=-1..1); H[7]:=int(l[7],x=-1..1);
>  H[8]:=int(l[8],x=-1..1);H[9]:=int(l[9],x=-1..1);
>  H[10]:=int(l[10],x=-1..1);
> 

                      H[6] := 0.295524224714752


                      H[7] := 0.269266719309997


                      H[8] := 0.219086362515982


                      H[9] := 0.149451349150581


                     H[10] := 0.0666713443086875

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