Difference between revisions of "Manuals/calci/ERF"

 
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<div style="font-size:30px">'''ERF(ll,ul)'''</div><br/>
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<div style="font-size:30px">'''ERF(a,b,accuracy)'''</div><br/>
*<math>ll</math> is the lower limit and <math> ul </math> is the upper limit.
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*<math>a</math> is the lower limit and <math> b </math> is the upper limit.
 
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*<math>accuracy</math>  gives accurate value of the solution
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**ERF(), returns the Error Function.
  
 
==Description==
 
==Description==
 
*This function gives the value of the error function .  
 
*This function gives the value of the error function .  
 
*Error function is the special function which is encountered in integrating the normal distribution.
 
*Error function is the special function which is encountered in integrating the normal distribution.
*In <math>ERF(ll,ul),ll</math> is the lower limit of the integrating function and <math>ul</math> is the upper limit of the integrating function.
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*In <math>ERF(a,b,accuracy)</math>,<math>a</math> is the lower limit of the integrating function and <math>b</math> is the upper limit of the integrating function.
*Also <math>ul</math> is optional. When we are omitting the <math>ul</math> value, then the  integral of the error function between 0 and the given <math>ll</math> value is returned otherwise it will consider the given <math>ll</math> and <math>ul</math> values.  
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*Also <math>b</math> is optional. When we are omitting the <math>b</math> value, then the  integral of the error function between 0 and the given <math>a</math> value is returned otherwise it will consider the given <math>a</math> and <math>b</math> values.  
 
*This function is also called Gauss error function.
 
*This function is also called Gauss error function.
 
*<math>ERF </math>is defined by:<math>ERF(z)=\frac {2}{\sqrt{\pi}}\int\limits_{0}^{z}e^{-t^2} dt</math>         
 
*<math>ERF </math>is defined by:<math>ERF(z)=\frac {2}{\sqrt{\pi}}\int\limits_{0}^{z}e^{-t^2} dt</math>         
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*This function will return the result as error when  
 
*This function will return the result as error when  
 
  1.any one of the argument is non-numeric.
 
  1.any one of the argument is non-numeric.
  2.<math>ll</math> or <math>ul</math> is negative.
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  2.<math>a</math> or <math>b</math> is negative.
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==ZOS==
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*The syntax is to calculate error function in ZOS is <math>ERF(a,b,accuracy)</math>.
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**<math>a</math> is the lower limit and <math> b </math> is the upper limit.
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**<math>accuracy</math>  gives accurate value of the solution.
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*For e.g.,ERF(2,3),ERF(2,3,0.001)
  
 
==Examples==
 
==Examples==
#ERF(1,2)=0.15262153
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#ERF(1,2)=0.15262147206923793
#ERF(3,2)=-0.004655645
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#ERF(3,2)=0.004655644484048649
#ERF(0,1)=0.842700735
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#ERF(0,1)=0.8427007929497148
#ERF(5)=1
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#ERF(5)=0.9999999999984626
#ERF(-3)=NAN
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#ERF(-3)=-0.9999779095030014
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==Related Videos==
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{{#ev:youtube|PBSFXukqztU|280|center|Error Function}}
  
 
==See Also==
 
==See Also==
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==References==
 
==References==
 
[http://en.wikipedia.org/wiki/Error_function Error Function]
 
[http://en.wikipedia.org/wiki/Error_function Error Function]
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*[[Z_API_Functions | List of Main Z Functions]]
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*[[ Z3 |  Z3 home ]]

Latest revision as of 04:11, 29 September 2021

ERF(a,b,accuracy)


  • is the lower limit and is the upper limit.
  • gives accurate value of the solution
    • ERF(), returns the Error Function.

Description

  • This function gives the value of the error function .
  • Error function is the special function which is encountered in integrating the normal distribution.
  • In  ,  is the lower limit of the integrating function and   is the upper limit of the integrating function.
  • Also   is optional. When we are omitting the   value, then the integral of the error function between 0 and the given   value is returned otherwise it will consider the given   and   values.
  • This function is also called Gauss error function.
  •  is defined by: 
  •  .
  • In this case   is the lower limit and   is the upper limit.
  • This function will return the result as error when
1.any one of the argument is non-numeric.
2.  or   is negative.

ZOS

  • The syntax is to calculate error function in ZOS is  .
    •   is the lower limit and   is the upper limit.
    •   gives accurate value of the solution.
  • For e.g.,ERF(2,3),ERF(2,3,0.001)

Examples

  1. ERF(1,2)=0.15262147206923793
  2. ERF(3,2)=0.004655644484048649
  3. ERF(0,1)=0.8427007929497148
  4. ERF(5)=0.9999999999984626
  5. ERF(-3)=-0.9999779095030014

Related Videos

Error Function

See Also

References

Error Function