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  1. "File RECUREQN.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
  2.  
  3. LIN1_DIFFERENCE(p,q,x,x0,y0):=PRODUCT(p,x,x0,x-1)*(y0+SUM(q/PRODUCT(p,x,x0,x),~
  4. x,x0,x-1))
  5.  
  6. RECURRENCE1(r,x,y,x0,y0,n):=ITERATES([1+ELEMENT(v_,1),LIM(r,[x,y],v_)],v_,[x0,~
  7. y0],n)
  8.  
  9. GEOMETRIC1(k,p,q,x,x0,y0):=LIM(LIN1_DIFFERENCE(LIM(p,x,k^x),LIM(q,x,k^x),x,LOG~
  10. (x0,k),y0),x,LOG(x,k))
  11.  
  12. CLAIRAUT_DIF(p,q,d,x,y,c):=LIM(p-q,d,c)=0
  13.  
  14. LIN_SOLVE(a,b):=ELEMENT(ROW_REDUCE(a,b)`,1+DIMENSION(a))
  15.  
  16. LIN2_CCF_HOM_AUX(b,x):=IF(b<0, -COS(pi*x)*(-b)^x, b^x)
  17.  
  18. LIN2_CCF_HOM(p,q,d,x):=~
  19.  IF(d=0, [(-p/2)^x, x*(-p/2)^x],~
  20.     IF(d>0,[LIN2_CCF_HOM_AUX((-p+SQRT(d))/2,x),~
  21.         LIN2_CCF_HOM_AUX((-p-SQRT(d))/2,x)],~
  22.        ((p^2-d)/4)^(x/2)*[SIN(x*ATAN(SQRT(-d),-p)),COS(x*ATAN(SQRT(-d),-p))]),~
  23.        ((p^2-d)/4)^(x/2)*[SIN(x*ATAN(SQRT(-d),-p)),COS(x*ATAN(SQRT(-d),-p))])
  24.  
  25. LIN2_CCF_PARTIC(h,r,x):=~
  26.  h . SUM(r LIM([-ELEMENT(h,2),ELEMENT(h,1)]/DET([h,LIM(h,x,x+1)]),x,x+1),x)
  27.  
  28. LIN2_CCF_AUX(h,r,x,c):= c . h + LIN2_CCF_PARTIC(h,r,x)
  29.  
  30. LIN2_CCF(p,q,r,x,c1,c2):=~
  31.   LIN2_CCF_AUX(LIN2_CCF_HOM(p,q,p^2-4q,x),r,x,[c1,c2])
  32.  
  33. LIN2_CCF_BV_AUX2(h,p,x,x0,y0,x2,y2):=~
  34.  p + h . LIN_SOLVE([LIM(h,x,x0),LIM(h,x,x2)],[y0-LIM(p,x,x0),y2-LIM(p,x,x2)])
  35.  
  36. LIN2_CCF_BV_AUX(h,r,x,x0,y0,x2,y2):=~
  37.  LIN2_CCF_BV_AUX2(h,LIN2_CCF_PARTIC(h,r,x),x,x0,y0,x2,y2)
  38.  
  39. LIN2_CCF_BV(p,q,r,x,x0,y0,x2,y2):=~
  40.  LIN2_CCF_BV_AUX(LIN2_CCF_HOM(p,q,p^2-4q,x),r,x,x0,y0,x2,y2)
  41.