Biểu thức 13: "K" equals left bracket, 0...1 7 , right bracketK=0...17
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Biểu thức 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 parenthesisfx=sechx14+12sin3πtanhx4
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Biểu thức 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 , EndFractionCT=∫∞−∞TK,xfx1+x2dx∫∞−∞TK,x21+x2dx
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Biểu thức 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 , EndFractionCU=∫∞−∞UK,xfx1+x2dx∫∞−∞UK,x21+x2dx
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Biểu thức 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 parenthesisN∑n=0CTn+1Tn,x
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Biểu thức 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 parenthesisN∑n=0CUn+1Un,x
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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)
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Biểu thức 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 , EndFractionCT2=∫∞−∞TK,xfx1+x21+adx∫∞−∞TK,x21+x2dx
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Biểu thức 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 , EndFractionCU2=∫∞−∞UK,xfx1+x21+adx∫∞−∞UK,x21+x2dx
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Biểu thức 22: "a" equals negative 0.3 3a=−0.33
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Biểu thức 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 , BaselineN∑n=0CT2n+1Tn,x1+x2a
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Biểu thức 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 , BaselineN∑n=0CU2n+1Un,x1+x2a
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Coefficients can also using a truncated fourier transform of f(tan(pi/2*x)) on (-1,1)
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cung cấp bởi
cung cấp bởi
"x"x
"y"y
"a" squareda2
"a" Superscript, "b" , Baselineab
77
88
99
over÷
chức năng
((
))
less than<
greater than>
44
55
66
times×
| "a" ||a|
,,
less than or equal to≤
greater than or equal to≥
11
22
33
negative−
A B C
StartRoot, , EndRoot
piπ
00
..
equals=
positive+
hoặc
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