未命名图表 | Desmos

表达式13: "K" equals left bracket, 0...1 7 , right bracket

equals

18个元素列表

表达式14: "f" left parenthesis, "x" , right parenthesis equals hyperbolic secant left parenthesis, "x" , right parenthesis left parenthesis, 1 quarter plus 1 half sin left parenthesis, 3 pi tanh left parenthesis, StartFraction, "x" Over 4 , EndFraction , right parenthesis , right parenthesis , right parenthesis

表达式15: "C" Subscript, "T" , Baseline equals StartFraction, left parenthesis, Start integral from negative infinity to infinity , end integral, StartNestedFraction, "T" left parenthesis, "K" , "x" , right parenthesis "f" left parenthesis, "x" , right parenthesis NestedOver left parenthesis, 1 plus "x" squared , right parenthesis , EndNestedFraction "d" "x" , right parenthesis Over left parenthesis, Start integral from negative infinity to infinity , end integral, StartNestedFraction, "T" left parenthesis, "K" , "x" , right parenthesis squared NestedOver left parenthesis, 1 plus "x" squared , right parenthesis , EndNestedFraction "d" "x" , right parenthesis , EndFraction

equals

0.1 3 9 9 4 8 2 3 7 2 0 5

0.1 1 9 8 7 5 4 8 7 1 2 2

negative 0.1 2 9 0 8 7 8 6 8 4 6 9

negative 0.2 6 3 3 9 2 7 5 3 9 2 5

negative 0.0 2 0 0 0 8 2 8 9 1 0 7 6

0.1 3 2 4 9 1 8 6 5 8 5 2

0.0 0 0 7 4 0 0 1 9 3 7 9 4 9 5

0.0 6 1 7 1 7 8 5 2 0 6 7 2

0.0 0 3 2 0 8 5 3 0 2 4 8 2

negative 0.0 1 4 4 6 3 3 6 6 9 1 5 2

0.0 0 2 4 5 4 2 8 7 3 3 5 0 7

negative 0.0 2 9 9 1 0 1 7 1 9 7 1 4

0.0 0 1 5 0 5 1 8 4 2 1 0 6

negative 0.0 1 7 5 7 9 8 6 8 9 1 7 3

0.0 0 0 8 3 4 2 9 0 2 8 8 9 6 1

18个元素列表

表达式16: "C" Subscript, "U" , Baseline equals StartFraction, left parenthesis, Start integral from negative infinity to infinity , end integral, StartNestedFraction, "U" left parenthesis, "K" , "x" , right parenthesis "f" left parenthesis, "x" , right parenthesis NestedOver left parenthesis, 1 plus "x" squared , right parenthesis , EndNestedFraction "d" "x" , right parenthesis Over left parenthesis, Start integral from negative infinity to infinity , end integral, StartNestedFraction, "U" left parenthesis, "K" , "x" , right parenthesis squared NestedOver left parenthesis, 1 plus "x" squared , right parenthesis , EndNestedFraction "d" "x" , right parenthesis , EndFraction

equals

0.2 3 4 5 2 7 8 0 0 2 3 6

0.2 1 7 6 6 7 6 7 4 5 0 7

negative 0.0 2 8 8 0 0 2 1 1 5 0 2 8

negative 0.2 3 2 4 1 3 9 2 6 3 7 1

negative 0.0 1 8 9 3 5 0 3 4 2 2 0 9

0.0 1 3 3 0 7 2 1 7 1 0 1 9

negative 0.0 0 7 5 5 7 8 2 5 1 1 9 9 6

0.0 6 2 5 0 4 1 3 8 6 7 6

negative 0.0 0 2 4 5 9 6 8 3 8 1 6 9 7

0.0 2 7 7 1 7 6 0 3 3 6 7 1

negative 0.0 0 0 5 0 1 6 5 0 0 1 8 8 9 1

negative 0.0 0 3 2 0 4 2 1 0 3 4 9 1 9

0.0 0 0 1 6 7 4 2 4 8 5 8 5 8 6

negative 0.0 1 3 5 7 6 4 1 9 6 2 3 6

0.0 0 0 3 3 7 5 4 3 4 6 5 4 6 4

18个元素列表

表达式17: Start sum from "n" equals 0 to "N" , end sum, left parenthesis, "C" Subscript, "T" , Baseline left bracket, "n" plus 1 , right bracket "T" left parenthesis, "n" , "x" , right parenthesis , right parenthesis

表达式18: Start sum from "n" equals 0 to "N" , end sum, left parenthesis, "C" Subscript, "U" , Baseline left bracket, "n" plus 1 , right bracket "U" left parenthesis, "n" , "x" , right parenthesis , right parenthesis

You can tweak the weight function in the numerator and then apply the reciprocal of the modified version to change asymptotic behavior or tradeoff error in different intervals (so long as it doesn't break convergence)

表达式20: "C" Subscript, "T" 2 , Baseline equals StartFraction, left parenthesis, Start integral from negative infinity to infinity , end integral, StartNestedFraction, "T" left parenthesis, "K" , "x" , right parenthesis "f" left parenthesis, "x" , right parenthesis NestedOver left parenthesis, 1 plus "x" squared , right parenthesis Superscript, left parenthesis, 1 plus "a" , right parenthesis , Baseline , EndNestedFraction "d" "x" , right parenthesis Over left parenthesis, Start integral from negative infinity to infinity , end integral, StartNestedFraction, "T" left parenthesis, "K" , "x" , right parenthesis squared NestedOver left parenthesis, 1 plus "x" squared , right parenthesis , EndNestedFraction "d" "x" , right parenthesis , EndFraction

equals

0.1 6 2 4 3 3 1 3 3 3 0 7

0.1 2 3 2 7 5 3 3 3 1 3 2

negative 0.1 2 1 2 0 1 9 1 2 0 1 6

negative 0.2 9 4 4 9 8 8 7 0 5 1 1

negative 0.0 4 2 2 6 9 3 4 5 7 8 3 8

0.1 4 3 6 1 7 9 9 4 3 8 7

negative 0.0 0 9 3 0 9 8 1 7 7 5 0 9

0.0 9 9 5 8 3 6 1 4 1 6 6 2

0.0 0 0 6 4 2 4 6 6 4 4 4 2 4 3

negative 0.0 0 6 5 7 8 5 3 6 1 6 4 8 5

0.0 0 2 7 9 2 3 4 6 1 6 0 0 7

negative 0.0 4 4 7 0 7 5 4 7 4 7 8

0.0 0 2 6 3 2 2 9 7 5 4 4 1 4

negative 0.0 3 4 6 7 0 6 2 3 2 1 6 4

0.0 0 1 9 5 1 5 8 2 6 8 1 0 5

18个元素列表

表达式21: "C" Subscript, "U" 2 , Baseline equals StartFraction, left parenthesis, Start integral from negative infinity to infinity , end integral, StartNestedFraction, "U" left parenthesis, "K" , "x" , right parenthesis "f" left parenthesis, "x" , right parenthesis NestedOver left parenthesis, 1 plus "x" squared , right parenthesis Superscript, left parenthesis, 1 plus "a" , right parenthesis , Baseline , EndNestedFraction "d" "x" , right parenthesis Over left parenthesis, Start integral from negative infinity to infinity , end integral, StartNestedFraction, "U" left parenthesis, "K" , "x" , right parenthesis squared NestedOver left parenthesis, 1 plus "x" squared , right parenthesis , EndNestedFraction "d" "x" , right parenthesis , EndFraction

equals

0.2 6 2 0 8 6 4 6 3 4 2 6

0.2 3 3 2 6 1 3 7 2 7 3 7

0.0 0 0 4 1 9 4 0 5 5 7 8 9 6 4

negative 0.2 6 5 2 8 9 5 3 1 3 1 8

negative 0.0 2 0 5 0 6 5 4 2 1 1 5 6

negative 0.0 0 8 1 6 9 8 6 4 2 9 5 0 1

negative 0.0 1 3 5 8 7 0 6 2 6 4 2 8

0.0 8 5 7 3 0 9 9 4 4 9 7 8

negative 0.0 0 6 9 4 3 4 8 5 0 1 8 5 5

0.0 5 3 0 2 0 0 7 5 5 0 0 8

negative 0.0 0 3 0 3 9 1 0 6 3 0 3 9 9

0.0 0 4 7 7 1 7 3 2 3 9 6 6 2

negative 0.0 0 1 0 2 8 3 0 3 6 8 2 2 3

negative 0.0 1 9 3 1 8 1 7 8 5 9 0 4

negative 0.0 0 0 0 8 2 0 9 9 9 4 1 8 9 5 7

18个元素列表

表达式22: "a" equals negative 0.3 3

negative 1

表达式23: Start sum from "n" equals 0 to "N" , end sum, left parenthesis, "C" Subscript, "T" 2 , Baseline left bracket, "n" plus 1 , right bracket "T" left parenthesis, "n" , "x" , right parenthesis , right parenthesis left parenthesis, 1 plus "x" squared , right parenthesis Superscript, left parenthesis, "a" , right parenthesis , Baseline

表达式24: Start sum from "n" equals 0 to "N" , end sum, left parenthesis, "C" Subscript, "U" 2 , Baseline left bracket, "n" plus 1 , right bracket "U" left parenthesis, "n" , "x" , right parenthesis , right parenthesis left parenthesis, 1 plus "x" squared , right parenthesis Superscript, left parenthesis, "a" , right parenthesis , Baseline

Coefficients can also using a truncated fourier transform of f(tan(pi/2*x)) on (-1,1)

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