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-1.000000000000000210 774 1.0 1.000000000000000210 -1.0 1.000000000000000210 775 1.0 1.000000000000000210 -1.0 -1.000000000000000210 776 1.0 1.000000000000000210 -1.0 1.000000000000000210 777 1.0 1.000000000000000210 -1.0 -1.000000000000000210 producting function with right calculations alpha= 0.96 z= 1.00 producting function= 24.99999999999999980 586 24.99999999999999980 24.99999999902016310 -0.00000000097983676 alpha= 0.96 z= 0.99 producting function= 6.93375245281536403 406 6.93375245281536403 6.93375245202377813 -0.00000000079158591 alpha= 0.96 z= 0.95 producting function= 3.20092199832239934 427 3.20092199832239934 3.20092199883072547 0.00000000050832613 alpha= 0.96 z= 0.90 producting function= 2.27272727272727273 377 2.27272727272727273 2.27272727172974845 -0.00000000099752428 alpha= 0.96 z= 0.80 producting function= 1.61039156600207715 386 1.61039156600207715 1.61039156599970813 -0.00000000000236902 alpha= 0.96 z= 0.50 producting function= 1.01977127056000523 396 1.01977127056000523 1.01977127145706379 0.00000000089705856 alpha= 0.96 z= 0.20 producting function= 0.80645161290322581 229 0.80645161290322581 0.80645161197090158 -0.00000000093232423 alpha= 0.96 z= 0.00 producting function= 0.72138732103095155 412 0.72138732103095155 0.72138732196486636 0.00000000093391480 alpha= 0.96 z= -0.20 producting function= 0.65857921221729031 315 0.65857921221729031 0.65857921181625980 -0.00000000040103051 alpha= 0.96 z= -0.50 producting function= 0.58909203703284133 385 0.58909203703284133 0.58909203612110289 -0.00000000091173844 alpha= 0.96 z= -0.80 producting function= 0.53778987964689770 320 0.53778987964689770 0.53778988031974956 0.00000000067285186 alpha= 0.96 z= -1.00 producting function= 0.51020408163265306 491 0.51020408163265306 0.51020408066617815 -0.00000000096647491 *) { to calculate right the values of the Legandre polinoms Pn(x) for any value x by using recurent formula without analytic operations } UNIT UnPolega ; INTERFACE Procedure TheSameButRight ; Procedure ProductButRight ; IMPLEMENTATION Uses UnForPrt , UnConTyp ; { for maxp global } { by the use recurent formula n*Pn(z)=(2*n-1)*z*P(n-1)(z)-(n-1)*P(n-2)(z), P0(z)=1, P1(z)=z } Procedure TheSameButRight ; Var i,n : word ; q,r : Extended ; x,p0,p1,p2 : Array[1..2] of Extended ; Begin x[1]:=+1.0; { two value for x } x[2]:=-1.0; WriteLn(PrtFile,' accurate formulae Pn(+1)=+1 , Pn(-1)=(-1)^n'); For i:=1 To 2 Do Begin { initial value for the Legandre polinoms } p0[i]:=1; p1[i]:=x[i]; End; For n:=2 To maxp Do { UnConTyp global } Begin q:=n; r:=1.0/q; For i:=1 To 2 Do p2[i]:=(2*q-1)*r*x[i]*p1[i]-(q-1)*r*p0[i]; { recurent formula } WriteLn(PrtFile,n:4,x[1]:5:1,p2[1]:24:18,x[2]:10:1,p2[2]:24:18); For i:=1 To 2 Do Begin p0[i]:=p1[i]; p1[i]:=p2[i]; End; End; End; Procedure FunctiProduct ( z , a : extended ) ; Var nn : word ; q,r : Extended ; aln : Extended ; va,vsum : Extended ; p0,p1,p2 : Extended ; bo : boolean ; Begin va:=1/Sqrt(1-2*a*z+Sqr(a)); vsum:=1+a*z; { two terms initial } WriteLn(PrtFile,' alpha=',a:10:2,' z=',z:10:2); writeln(prtfile,' producting function=',va:29:17); aln:=a; p0:=1; { initial value for Legandre polinom P0(x)=+1 } p1:=z; { initial value for Legandre polinom P1(x)=+x } bo:=False; { initial boolean } nn:=2; { initial word } while ( ( nn < maxp ) and ( not bo ) ) Do { uncontyp global } Begin q:=nn; r:=1.0/q; p2:=(2*q-1)*r*z*p1-(q-1)*r*p0; { recurent formula } aln:=a*aln; { the next power for alpha } vsum:=vsum+aln*p2; bo:= ( Abs(vsum-va) < 1.0e-12 ) ; { to compare } if bo then { our value } WriteLn(PrtFile,nn:4,va:23:17,vsum:23:17,(vsum-va):25:17); p0:=p1; { to replace } p1:=p2; { to replace } nn:=nn+1; { the next polinom order } End; End; Procedure ProductButRight ; var z,a : extended ; begin { value for alpha (r_0/r) } a:=0.96; { for alpha } { to calculate differencies } z:=1.00; { for z } FunctiProduct(z,a); z:=0.99; { for z } FunctiProduct(z,a); z:=0.95; { for z } FunctiProduct(z,a); z:=0.90; { for z } FunctiProduct(z,a); z:=0.80; { for z } FunctiProduct(z,a); z:=0.50; { for z } FunctiProduct(z,a); z:=0.20; { for z } FunctiProduct(z,a); z:=0.00; { for z } FunctiProduct(z,a); z:=-0.2; { for z } FunctiProduct(z,a); z:=-0.5; { for z } FunctiProduct(z,a); z:=-0.8; { for z } FunctiProduct(z,a); z:=-1.0; { for z } FunctiProduct(z,a); end; END.