Difference between revisions of "Manuals/calci/ERF"
Jump to navigation
Jump to search
| Line 10: | Line 10: | ||
*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> | ||
| − | <math>ERF(a,b)=\frac{2}{\sqrt{\pi}}\int\limits_{a}^{b}e^{-t^2} dt=ERF(b)-ERF(a)</math>. | + | *<math>ERF(a,b)=\frac{2}{\sqrt{\pi}}\int\limits_{a}^{b}e^{-t^2} dt=ERF(b)-ERF(a)</math>. |
*In this case 'a' is the lower limit and 'b' is the upper limit. | *In this case 'a' is the lower limit and 'b' is the upper limit. | ||
*This function will return the result as error when | *This function will return the result as error when | ||
Revision as of 23:11, 25 December 2013
ERF(ll,ul)
- 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 ll} 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 ul } 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 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 ul} 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 ul} 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 ul} 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 ll} 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 ll} 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 ul} 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 'a' is the lower limit and 'b' is the upper limit.
- This function will return the result as error when
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 ul}
is the upper limit of the integrating function.- any one of the argument is nonnumeric.
- ll or ul is negative.
Examples
- ERF(1,2)=0.15262153
- ERF(3,2)=-0.004655645
- ERF(0,1)=0.842700735
- ERF(5)=1
- ERF(-3)=NAN