1 | test_legendre = ->
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2 | run_test [
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3 | "legendre(x,n)",
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4 | "legendre(x,n,0)",
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5 |
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6 | "legendre(x,n,m)",
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7 | "legendre(x,n,m)",
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8 |
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9 | "legendre(x,0)-1",
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10 | "0",
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11 |
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12 | "legendre(x,1)-x",
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13 | "0",
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14 |
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15 | "legendre(x,2)-1/2*(3*x^2-1)",
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16 | "0",
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17 |
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18 | "legendre(x,3)-1/2*(5*x^3-3*x)",
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19 | "0",
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20 |
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21 | "legendre(x,4)-1/8*(35*x^4-30*x^2+3)",
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22 | "0",
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23 |
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24 | "legendre(x,5)-1/8*(63*x^5-70*x^3+15*x)",
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25 | "0",
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26 |
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27 | "legendre(x,6)-1/16*(231*x^6-315*x^4+105*x^2-5)",
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28 | "0",
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29 |
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30 | "legendre(x,0,0)-1",
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31 | "0",
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32 |
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33 | "legendre(x,1,0)-x",
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34 | "0",
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35 |
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36 | "legendre(x,1,1)+(1-x^2)^(1/2)",
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37 | "0",
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38 |
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39 | "legendre(x,2,0)-1/2*(3*x^2-1)",
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40 | "0",
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41 |
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42 | "legendre(x,2,1)+3*x*(1-x^2)^(1/2)",
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43 | "0",
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44 |
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45 | "legendre(x,2,2)-3*(1-x^2)",
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46 | "0",
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47 |
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48 | "legendre(x,3,0)-1/2*x*(5*x^2-3)",
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49 | "0",
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50 |
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51 | "legendre(x,3,1)-3/2*(1-5*x^2)*(1-x^2)^(1/2)",
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52 | "0",
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53 |
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54 | "legendre(x,3,2)-15*x*(1-x^2)",
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55 | "0",
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56 |
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57 | "legendre(x,3,3)+15*(1-x^2)^(3/2)",
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58 | "0",
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59 |
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60 | "legendre(x,4,0)-1/8*(35*x^4-30*x^2+3)",
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61 | "0",
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62 |
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63 | "legendre(x,4,1)-5/2*x*(3-7*x^2)*(1-x^2)^(1/2)",
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64 | "0",
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65 |
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66 | "legendre(x,4,2)-15/2*(7*x^2-1)*(1-x^2)",
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67 | "0",
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68 |
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69 | "legendre(x,4,3)+105*x*(1-x^2)^(3/2)",
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70 | "0",
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71 |
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72 | "legendre(x,4,4)-105*(1-x^2)^2",
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73 | "0",
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74 |
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75 | "legendre(x,5,0)-1/8*x*(63*x^4-70*x^2+15)",
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76 | "0",
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77 |
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78 | "legendre(cos(theta),0,0)-1",
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79 | "0",
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80 |
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81 | "legendre(cos(theta),1,0)-cos(theta)",
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82 | "0",
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83 |
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84 | "legendre(cos(theta),1,1)+abs(sin(theta))",
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85 | "0",
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86 |
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87 | "legendre(cos(theta),2,0)-1/2*(3*cos(theta)^2-1)",
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88 | "0",
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89 |
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90 | "legendre(cos(theta),2,1)+3*cos(theta)*abs(sin(theta))",
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91 | "0",
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92 |
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93 | "legendre(cos(theta),2,2)-3*sin(theta)^2",
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94 | "0",
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95 |
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96 | "legendre(cos(theta),3,0)-1/2*cos(theta)*(5*cos(theta)^2-3)",
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97 | "0",
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98 |
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99 | "legendre(cos(theta),3,1)- (3/2*abs(sin(theta))-15/2*cos(theta)^2*abs(sin(theta)))",
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100 | "0",
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101 |
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102 | "legendre(cos(theta),3,2)-15*cos(theta)*sin(theta)^2",
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103 | "0",
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104 |
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105 | "legendre(cos(theta),3,3)+15*(sin(theta)^2)^(3/2)",
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106 | "0",
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107 |
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108 | "legendre(a-b,10)-eval(subst(a-b,x,legendre(x,10)))",
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109 | "0",
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110 | ]
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