Difference between revisions of "Manuals/calci/ERF"

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*<math>a</math> is the lower limit and <math> b </math> is the upper limit.
 
*<math>a</math> is the lower limit and <math> b </math> is the upper limit.
 
*<math>accuracy</math>  gives accurate value of the solution
 
*<math>accuracy</math>  gives accurate value of the solution
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**ERF(), returns the Error Function.
  
 
==Description==
 
==Description==
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**<math>a</math> is the lower limit and <math> b </math> is the upper limit.
 
**<math>a</math> is the lower limit and <math> b </math> is the upper limit.
 
**<math>accuracy</math>  gives accurate value of the solution.
 
**<math>accuracy</math>  gives accurate value of the solution.
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*For e.g.,erf(2,3),erf(2,3,0.001)
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*For e.g.,ERF(2,3),ERF(2,3,0.001)
  
 
==Examples==
 
==Examples==
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#ERF(1,2)=0.15262153
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#ERF(1,2)=0.15262147206923793
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#ERF(3,2)=-0.004655645
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#ERF(3,2)=0.004655644484048649
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#ERF(0,1)=0.842700735
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#ERF(0,1)=0.8427007929497148
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#ERF(5)=1
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#ERF(5)=0.9999999999984626
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#ERF(-3)=NAN
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#ERF(-3)=-0.9999779095030014
  
 
==Related Videos==
 
==Related Videos==
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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 03:11, 29 September 2021

ERF(a,b,accuracy)


  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is the lower limit and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b } is the upper limit.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle accuracy} 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ERF(a,b,accuracy)} ,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is the lower limit of the integrating function and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} is the upper limit of the integrating function.
  • Also Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} is optional. When we are omitting the Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} value, then the integral of the error function between 0 and the given Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} value is returned otherwise it will consider the given Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} values.
  • This function is also called Gauss error function.
  • is defined by:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ERF(z)=\frac {2}{\sqrt{\pi}}\int\limits_{0}^{z}e^{-t^2} dt}
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ERF(a,b)=\frac{2}{\sqrt{\pi}}\int\limits_{a}^{b}e^{-t^2} dt=ERF(b)-ERF(a)} .
  • In this case Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is the lower limit and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} is the upper limit.
  • This function will return the result as error when
1.any one of the argument is non-numeric.
2.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a}
 or Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b}
 is negative.

ZOS

  • The syntax is to calculate error function in ZOS is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ERF(a,b,accuracy)} .
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} is the lower limit and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b } is the upper limit.
    • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle accuracy} 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



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