lepton

lepton

Expression name Meaning Detail explanation
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^ Power \(x^N\)
sqrt Square root \(\sqrt{x}\)
exp Exponential \(e^x\)
log Natural logarithm \(log(x)\)
erf Error function \(erf(x)=\frac{1}{\sqrt\pi}\int_{-x}^x e^{-t^2}\)
erfc Complementary error function \(erfc(x)= 1-erf(x)=\frac{2}{\sqrt{\pi}}\int_x^{\infty}e^{-t^2}\)
sin Sine (angle in radians)
cos Cosine (angle in radians)
sec Secant (angle in radians)
csc Cosecant (angle in radians)
tan Tangent (angle in radians)
cot Cotangent (angle in radians)
asin Inverse sine (in radians)
acos Inverse cosine (in radians)
atan Inverse tangent (in radians)
atan2 Two-argument inverse tangent (in radians)
sinh Hyperbolic sine
cosh Hyperbolic cosine
tanh Hyperbolic tangent
abs Absolute value
floor Floor
ceil Ceiling
min Minimum of two values
max Maximum of two values
delta delta(x)=1 if x=0, 0 otherwise \( \delta(x)=\begin{cases} 0 & x< 0 \newline 1 & x=0 \newline 0 & x> 0 \end{cases} \)
step step(x)=0 if x<0, 1 if x>=0 \(\theta(x)=\begin{cases} 0 & x< 0 \newline 1 & x\ge 0 \end{cases}\)
select select(x,y,z)=z if x=0, y otherwise \(select(x,y,z)= \begin{cases} z & x= 0 \newline y & x \ne 0 \end{cases}\)