4.32: Difference between revisions

From testwiki
Jump to navigation Jump to search
VisualWikitext
 
 
Line 14: Line 14:
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
|-  
|-  
| [https://dlmf.nist.gov/4.32.E1 4.32.E1] || [[Item:Q1854|<math>\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cosh(x) <= ((sinh(x))/(x))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cosh[x] <= (Divide[Sinh[x],x])^(3)</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| [https://dlmf.nist.gov/4.32.E1 4.32.E1] || <math qid="Q1854">\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cosh(x) <= ((sinh(x))/(x))^(3)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cosh[x] <= (Divide[Sinh[x],x])^(3)</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|-  
|-  
| [https://dlmf.nist.gov/4.32.E2 4.32.E2] || [[Item:Q1855|<math>\sin@@{x}\cos@@{x} < \tanh@@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@@{x}\cos@@{x} < \tanh@@{x}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>sin(x)*cos(x) < tanh(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[x]*Cos[x] < Tanh[x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| [https://dlmf.nist.gov/4.32.E2 4.32.E2] || <math qid="Q1855">\sin@@{x}\cos@@{x} < \tanh@@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@@{x}\cos@@{x} < \tanh@@{x}</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>sin(x)*cos(x) < tanh(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[x]*Cos[x] < Tanh[x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|-  
|-  
| [https://dlmf.nist.gov/4.32.E2 4.32.E2] || [[Item:Q1855|<math>\tanh@@{x} < x</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tanh@@{x} < x</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>tanh(x) < x</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tanh[x] < x</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| [https://dlmf.nist.gov/4.32.E2 4.32.E2] || <math qid="Q1855">\tanh@@{x} < x</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tanh@@{x} < x</syntaxhighlight> || <math>x > 0</math> || <syntaxhighlight lang=mathematica>tanh(x) < x</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tanh[x] < x</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|-  
|-  
| [https://dlmf.nist.gov/4.32.E3 4.32.E3] || [[Item:Q1856|<math>|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}</syntaxhighlight> || <math>x > 0, y > 0</math> || <syntaxhighlight lang=mathematica>abs(cosh(x)- cosh(y)) >= abs(x - y)*sqrt(sinh(x)*sinh(y))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[Cosh[x]- Cosh[y]] >= Abs[x - y]*Sqrt[Sinh[x]*Sinh[y]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
| [https://dlmf.nist.gov/4.32.E3 4.32.E3] || <math qid="Q1856">|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}</syntaxhighlight> || <math>x > 0, y > 0</math> || <syntaxhighlight lang=mathematica>abs(cosh(x)- cosh(y)) >= abs(x - y)*sqrt(sinh(x)*sinh(y))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Abs[Cosh[x]- Cosh[y]] >= Abs[x - y]*Sqrt[Sinh[x]*Sinh[y]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
|-  
|-  
| [https://dlmf.nist.gov/4.32.E4 4.32.E4] || [[Item:Q1857|<math>\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}</syntaxhighlight> || <math>x \geq 0</math> || <syntaxhighlight lang=mathematica>arctan(x) <= (1)/(2)*Pi*tanh(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[x] <= Divide[1,2]*Pi*Tanh[x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| [https://dlmf.nist.gov/4.32.E4 4.32.E4] || <math qid="Q1857">\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}</syntaxhighlight> || <math>x \geq 0</math> || <syntaxhighlight lang=mathematica>arctan(x) <= (1)/(2)*Pi*tanh(x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>ArcTan[x] <= Divide[1,2]*Pi*Tanh[x]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|}
|}
</div>
</div>

Latest revision as of 11:09, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
4.32.E1 cosh ⁡ x ≤ ( sinh ⁡ x x ) 3 𝑥 superscript 𝑥 𝑥 3 {\displaystyle{\displaystyle\cosh x\leq\left(\frac{\sinh x}{x}\right)^{3}}}
\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}		 

cosh(x) <= ((sinh(x))/(x))^(3)

Cosh[x] <= (Divide[Sinh[x],x])^(3)
Failure Failure Successful [Tested: 3] Successful [Tested: 3]
4.32.E2 sin ⁡ x ⁢ cos ⁡ x < tanh ⁡ x 𝑥 𝑥 𝑥 {\displaystyle{\displaystyle\sin x\cos x<\tanh x}}
\sin@@{x}\cos@@{x} < \tanh@@{x}		 x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}} 
sin(x)*cos(x) < tanh(x)

Sin[x]*Cos[x] < Tanh[x]
Failure Failure Successful [Tested: 3] Successful [Tested: 3]
4.32.E2 tanh ⁡ x < x 𝑥 𝑥 {\displaystyle{\displaystyle\tanh x<x}}
\tanh@@{x} < x		 x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}} 
tanh(x) < x

Tanh[x] < x
Failure Failure Successful [Tested: 3] Successful [Tested: 3]
4.32.E3 | cosh ⁡ x - cosh ⁡ y | ≥ | x - y | ⁢ sinh ⁡ x ⁢ sinh ⁡ y 𝑥 𝑦 𝑥 𝑦 𝑥 𝑦 {\displaystyle{\displaystyle|\cosh x-\cosh y|\geq|x-y|\sqrt{\sinh x\sinh y}}}
|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}		 x > 0 , y > 0 formulae-sequence 𝑥 0 𝑦 0 {\displaystyle{\displaystyle x>0,y>0}} 
abs(cosh(x)- cosh(y)) >= abs(x - y)*sqrt(sinh(x)*sinh(y))

Abs[Cosh[x]- Cosh[y]] >= Abs[x - y]*Sqrt[Sinh[x]*Sinh[y]]
Failure Failure Successful [Tested: 9] Successful [Tested: 9]
4.32.E4 arctan ⁡ x ≤ 1 2 ⁢ π ⁢ tanh ⁡ x 𝑥 1 2 𝜋 𝑥 {\displaystyle{\displaystyle\operatorname{arctan}x\leq\tfrac{1}{2}\pi\tanh x}}
\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}		 x ≥ 0 𝑥 0 {\displaystyle{\displaystyle x\geq 0}} 
arctan(x) <= (1)/(2)*Pi*tanh(x)

ArcTan[x] <= Divide[1,2]*Pi*Tanh[x]
Failure Failure Successful [Tested: 3] Successful [Tested: 3]
Retrieved from "https://lct.wmflabs.org/w/index.php?title=4.32&oldid=58100"