1 | ###
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2 | Laguerre function
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3 |
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4 | Example
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5 |
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6 | laguerre(x,3)
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7 |
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8 | Result
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9 |
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10 | 1 3 3 2
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11 | - --- x + --- x - 3 x + 1
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12 | 6 2
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13 |
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14 | The computation uses the following recurrence relation.
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15 |
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16 | L(x,0,k) = 1
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17 |
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18 | L(x,1,k) = -x + k + 1
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19 |
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20 | n*L(x,n,k) = (2*(n-1)+1-x+k)*L(x,n-1,k) - (n-1+k)*L(x,n-2,k)
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21 |
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22 | In the "for" loop i = n-1 so the recurrence relation becomes
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23 |
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24 | (i+1)*L(x,n,k) = (2*i+1-x+k)*L(x,n-1,k) - (i+k)*L(x,n-2,k)
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25 | ###
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26 |
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27 |
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28 |
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29 | Eval_laguerre = ->
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30 | # 1st arg
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31 |
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32 | push(cadr(p1))
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33 | Eval()
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34 |
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35 | # 2nd arg
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36 |
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37 | push(caddr(p1))
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38 | Eval()
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39 |
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40 | # 3rd arg
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41 |
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42 | push(cadddr(p1))
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43 | Eval()
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44 |
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45 | p2 = pop()
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46 | if (p2 == symbol(NIL))
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47 | push_integer(0)
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48 | else
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49 | push(p2)
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50 |
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51 | laguerre()
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52 |
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53 | #define X p1
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54 | #define N p2
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55 | #define K p3
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56 | #define Y p4
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57 | #define Y0 p5
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58 | #define Y1 p6
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59 |
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60 | laguerre = ->
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61 | n = 0
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62 | save()
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63 |
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64 | p3 = pop()
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65 | p2 = pop()
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66 | p1 = pop()
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67 |
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68 | push(p2)
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69 | n = pop_integer()
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70 |
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71 | if (n < 0 || isNaN(n))
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72 | push_symbol(LAGUERRE)
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73 | push(p1)
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74 | push(p2)
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75 | push(p3)
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76 | list(4)
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77 | restore()
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78 | return
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79 |
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80 | if (issymbol(p1))
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81 | laguerre2(n)
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82 | else
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83 | p4 = p1; # do this when p1 is an expr
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84 | p1 = symbol(SECRETX)
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85 | laguerre2(n)
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86 | p1 = p4
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87 | push(symbol(SECRETX))
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88 | push(p1)
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89 | subst()
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90 | Eval()
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91 |
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92 | restore()
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93 |
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94 | laguerre2 = (n) ->
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95 | i = 0
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96 |
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97 | push_integer(1)
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98 | push_integer(0)
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99 |
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100 | p6 = pop()
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101 |
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102 | for i in [0...n]
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103 |
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104 | p5 = p6
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105 |
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106 | p6 = pop()
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107 |
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108 | push_integer(2 * i + 1)
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109 | push(p1)
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110 | subtract()
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111 | push(p3)
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112 | add()
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113 | push(p6)
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114 | multiply()
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115 |
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116 | push_integer(i)
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117 | push(p3)
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118 | add()
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119 | push(p5)
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120 | multiply()
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121 |
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122 | subtract()
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123 |
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124 | push_integer(i + 1)
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125 | divide()
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126 |
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127 |
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