Difference between revisions of "Manuals/calci/ERF"
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*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(a,b,accuracy),<math>a</math> is the lower limit of the integrating function and <math>b</math> is the upper limit of the integrating function. | + | *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>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. | *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. | ||
Revision as of 02:12, 3 July 2014
ERF(a,b,accuracy)
- 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
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.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.
- 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 } 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 Section
- 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
- ERF(1,2)=0.15262153
- ERF(3,2)=-0.004655645
- ERF(0,1)=0.842700735
- ERF(5)=1
- ERF(-3)=NAN