Difference between revisions of "Predefined Functions and Operators"

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(Created page with "beta(a, b) Returns the beta function Β(a, b) http://mathworld.wolfram.com/BetaFunction.html beta(a, b, x) Returns the incomplete beta function Β(x;a, b) http://mathworld.wolfr...")
 
(Lambert's W function)
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beta(a, b)
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<noinclude>{{Manual Page|version=5.0}}</noinclude>
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Returns the beta function Β(a, b)
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To create numbers, coordinates, or equations using the [[Input Bar]] you may also use the following pre-defined functions and operations. Logic operators and functions are listed in article about [[Boolean values]].
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http://mathworld.wolfram.com/BetaFunction.html
 
  
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beta(a, b, x)
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{{Note|The predefined functions need to be entered using parentheses. You must not put a space between the function name and the parentheses.}}
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Returns the incomplete beta function Β(x;a, b)
 
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http://mathworld.wolfram.com/IncompleteBetaFunction.html
 
  
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betaRegularized(a, b, x)
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Returns the incomplete regularized beta function I(x; a, b)
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{| class="pretty" width="95%"
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http://mathworld.wolfram.com/RegularizedBetaFunction.html
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|-
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!Operation / Function
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gamma(x)
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!Input
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Returns the gamma function Γ(x)
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|-
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http://mathworld.wolfram.com/GammaFunction.html
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|ℯ ([[w:E_(mathematical_constant)|Euler's number]])
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| {{KeyCode|Alt+e}}
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gamma(a, x)
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|-
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Returns the (lower) incomplete gamma function  γ(a, x)
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|ί ([[w:Imaginary unit|Imaginary unit]])
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http://mathworld.wolfram.com/IncompleteGammaFunction.html
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| {{KeyCode|Alt+i}}
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|-
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gammaRegularized(a, x)
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|π
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Returns the (lower) incomplete regularized gamma function P(a, x)
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| {{KeyCode|Alt+p}} or pi
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http://mathworld.wolfram.com/RegularizedGammaFunction.html
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|-
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|° ([[w:Degree symbol|Degree symbol]])
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| {{KeyCode|Alt+o}} or deg
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|-
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|Addition
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| +
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|-
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|Subtraction
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| -
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|-
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|Multiplication
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|* or Space key
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|-
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|Scalar product
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|* or Space key
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|-
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|Vector product(see [[Points and Vectors#Vector Product|Points and Vectors]])
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|⊗
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|-
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|Division
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|/
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|-
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|Exponentiation
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|^ or superscript (<code>x^2</code> or <code>x<sup>2</sup></code>)
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|-
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|Factorial
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|!
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|-
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|Parentheses
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|( )
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|-
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|x-coordinate
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|x( )
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|-
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|y-coordinate
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|y( )
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|-
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|z-coordinate
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|z( )
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|-
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|Argument (also works for 3D points / vectors)
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|arg( )
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|-
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|Conjugate
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|conjugate( )
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|-
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|[[Real_Function|Real]]
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|real( )
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|-
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|[[Imaginary_Function|Imaginary]]
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|imaginary( )
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|-
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|Absolute value
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|abs( )
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|-
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|Altitude angle (for 3D points / vectors)
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|alt( )
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|-
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|Sign
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|sgn( ) or sign()
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|-
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|Greatest integer less than or equal
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|floor( )
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|-
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|Least integer greater than or equal
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|ceil( )
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|-
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|Round
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|round( )
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|-
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|Square root
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|sqrt( )
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|-
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|Cubic root
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|cbrt( )
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|-
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| The nth root of x
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| nroot(x, n)
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|-
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|Random number between 0 and 1
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|random( )
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|-
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|Exponential function
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|exp( ) or ℯ<sup>x</sup>
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|-
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|Logarithm (natural, to base e)
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|ln( ) or log( )
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|-
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|Logarithm to base 2
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|ld( )
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|-
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|Logarithm to base 10
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|lg( )
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|-
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|Logarithm of ''x'' to base ''b''
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|log(b, x )
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|-
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|Cosine
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|cos( )
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|-
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|Sine
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|sin( )
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|-
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|Tangent
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|tan( )
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|-
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|Secant
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|sec()
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|-
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|Cosecant
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|cosec()
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|-
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|Cotangent
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|cot() or cotan()
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|-
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|Arc cosine (answer in radians)
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|acos( ) or arccos( )
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|-
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|Arc cosine (answer in degrees)
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|acosd( )
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|-
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|Arc sine (answer in radians)
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|asin( ) or arcsin( )
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|-
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|Arc sine (answer in degrees)
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|asind( )
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|-
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|Arc tangent (answer in radians, between -π/2 and π/2)
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|atan( ) or arctan( )
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|-
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|Arc tangent (answer in degrees, between -90° and 90°)
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|atand( )
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|-
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|[http://en.wikipedia.org/wiki/Atan2 Arc tangent (answer in radians, between -π and π)]
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|atan2(y, x) or arcTan2(y, x)
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|-
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|[http://en.wikipedia.org/wiki/Atan2 Arc tangent (answer in degrees, between -180° and 180°)]
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|atan2d(y, x)
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|-
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|Hyperbolic cosine
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|cosh( )
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|-
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|Hyperbolic sine
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|sinh( )
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|-
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|Hyperbolic tangent
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|tanh( )
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|-
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|Hyperbolic secant
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|sech( )
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|-
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|Hyperbolic cosecant
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|cosech( )
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|-
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|Hyperbolic cotangent
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|coth( ) or cotanh()
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|-
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|Antihyperbolic cosine
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|acosh( ) or arccosh( )
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|-
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|Antihyperbolic sine
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|asinh( ) or arcsinh( )
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|-
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|Antihyperbolic tangent
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|atanh( ) or arctanh( )
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|-
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|[http://mathworld.wolfram.com/BetaFunction.html Beta function] Β(a, b)
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|beta(a, b)
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|-
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|[http://mathworld.wolfram.com/IncompleteBetaFunction.html Incomplete beta function] Β(x;a, b)
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|beta(a, b, x)
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|-
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|[http://mathworld.wolfram.com/RegularizedBetaFunction.html Incomplete regularized beta function] I(x; a, b)
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|betaRegularized(a, b, x)
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|-
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|[[w:Gamma function|Gamma function Γ(x)]]
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|gamma( x)
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|-
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| (Lower) [http://mathworld.wolfram.com/IncompleteGammaFunction.html incomplete gamma function]  γ(a, x)
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|gamma(a, x)
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|-
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|(Lower)  [http://mathworld.wolfram.com/RegularizedGammaFunction.html incomplete regularized gamma function P(a,x) = γ(a, x) / Γ(a) ]
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|gammaRegularized(a, x)
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|-
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|[[w:Error_function|Gaussian Error Function]]
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|erf(x)
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|-
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| [[w:Digamma_function|Digamma function]]
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| psi(x)
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|-
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| The [http://en.wikipedia.org/wiki/Polygamma_function Polygamma function] is the (m+1)th derivative of the natural logarithm of the [http://en.wikipedia.org/wiki/Gamma_function Gamma function, gamma(x)] (m=0,1)
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| polygamma(m, x)
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|-
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| The [http://mathworld.wolfram.com/SineIntegral.html Sine Integral] function
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| sinIntegral(x)
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|-
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| The [http://mathworld.wolfram.com/CosineIntegral.html Cosine Integral] function
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| cosIntegral(x)
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|-
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| The [http://mathworld.wolfram.com/ExponentialIntegral.html Exponential Integral] function
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| expIntegral(x)
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|-
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| The [http://en.wikipedia.org/wiki/Riemann_zeta_function Riemann-Zeta] function ζ(x)
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| zeta(x)
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|-
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| [https://en.wikipedia.org/wiki/Lambert_W_function Lambert's W function] LambertW(x, branch)
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| LambertW(x, 0), LambertW(x, -1)
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|}
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{{note|The x, y, z operators can be used to get corresponding coefficients of a line.}}

Revision as of 13:46, 14 January 2019


To create numbers, coordinates, or equations using the Input Bar you may also use the following pre-defined functions and operations. Logic operators and functions are listed in article about Boolean values.

Note: The predefined functions need to be entered using parentheses. You must not put a space between the function name and the parentheses.


Operation / Function Input
ℯ (Euler's number) Alt + e
ί (Imaginary unit) Alt + i
π Alt + p or pi
° (Degree symbol) Alt + o or deg
Addition +
Subtraction -
Multiplication * or Space key
Scalar product * or Space key
Vector product(see Points and Vectors) ⊗
Division /
Exponentiation ^ or superscript (x^2 or x2)
Factorial !
Parentheses ( )
x-coordinate x( )
y-coordinate y( )
z-coordinate z( )
Argument (also works for 3D points / vectors) arg( )
Conjugate conjugate( )
Real real( )
Imaginary imaginary( )
Absolute value abs( )
Altitude angle (for 3D points / vectors) alt( )
Sign sgn( ) or sign()
Greatest integer less than or equal floor( )
Least integer greater than or equal ceil( )
Round round( )
Square root sqrt( )
Cubic root cbrt( )
The nth root of x nroot(x, n)
Random number between 0 and 1 random( )
Exponential function exp( ) or ℯx
Logarithm (natural, to base e) ln( ) or log( )
Logarithm to base 2 ld( )
Logarithm to base 10 lg( )
Logarithm of x to base b log(b, x )
Cosine cos( )
Sine sin( )
Tangent tan( )
Secant sec()
Cosecant cosec()
Cotangent cot() or cotan()
Arc cosine (answer in radians) acos( ) or arccos( )
Arc cosine (answer in degrees) acosd( )
Arc sine (answer in radians) asin( ) or arcsin( )
Arc sine (answer in degrees) asind( )
Arc tangent (answer in radians, between -π/2 and π/2) atan( ) or arctan( )
Arc tangent (answer in degrees, between -90° and 90°) atand( )
Arc tangent (answer in radians, between -π and π) atan2(y, x) or arcTan2(y, x)
Arc tangent (answer in degrees, between -180° and 180°) atan2d(y, x)
Hyperbolic cosine cosh( )
Hyperbolic sine sinh( )
Hyperbolic tangent tanh( )
Hyperbolic secant sech( )
Hyperbolic cosecant cosech( )
Hyperbolic cotangent coth( ) or cotanh()
Antihyperbolic cosine acosh( ) or arccosh( )
Antihyperbolic sine asinh( ) or arcsinh( )
Antihyperbolic tangent atanh( ) or arctanh( )
Beta function Β(a, b) beta(a, b)
Incomplete beta function Β(x;a, b) beta(a, b, x)
Incomplete regularized beta function I(x; a, b) betaRegularized(a, b, x)
Gamma function Γ(x) gamma( x)
(Lower) incomplete gamma function γ(a, x) gamma(a, x)
(Lower) incomplete regularized gamma function P(a,x) = γ(a, x) / Γ(a) gammaRegularized(a, x)
Gaussian Error Function erf(x)
Digamma function psi(x)
The Polygamma function is the (m+1)th derivative of the natural logarithm of the Gamma function, gamma(x) (m=0,1) polygamma(m, x)
The Sine Integral function sinIntegral(x)
The Cosine Integral function cosIntegral(x)
The Exponential Integral function expIntegral(x)
The Riemann-Zeta function ζ(x) zeta(x)
Lambert's W function LambertW(x, branch) LambertW(x, 0), LambertW(x, -1)
Note: The x, y, z operators can be used to get corresponding coefficients of a line.
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