# LiouvillianFunctionCategoryΒΆ

Category for the transcendental Liouvillian functions.

^: (%, %) -> %
acos: % -> %
acosh: % -> %
acot: % -> %
acoth: % -> %
acsc: % -> %
acsch: % -> %
asec: % -> %
asech: % -> %
asin: % -> %
asinh: % -> %
atan: % -> %
atanh: % -> %
Chi: % -> %

`Chi(x)` returns the hyperbolic cosine integral of `x`, i.e. the integral of `cosh(x) / x dx`.

Ci: % -> %

`Ci(x)` returns the cosine integral of `x`, i.e. the integral of `cos(x) / x dx`.

cos: % -> %
cosh: % -> %
cot: % -> %
coth: % -> %
csc: % -> %
csch: % -> %
dilog: % -> %

`dilog(x)` returns the dilogarithm of `x`, i.e. the integral of `log(x) / (1 - x) dx`.

Ei: % -> %

`Ei(x)` returns the exponential integral of `x`, i.e. the integral of `exp(x)/x dx`.

erf: % -> %

`erf(x)` returns the error function of `x`, i.e. `2 / sqrt(\%pi)` times the integral of `exp(-x^2) dx`.

erfi: % -> %

`erfi(x)` denotes `-\%i*erf(\%i*x)`

exp: % -> %
fresnelC: % -> %

fresnelC is the Fresnel integral `C`, defined by `C(x) = integrate(cos(\%pi*t^2/2), t=0..x)`

fresnelS: % -> %

fresnelS is the Fresnel integral `S`, defined by `S(x) = integrate(sin(\%pi*t^2/2), t=0..x)`

integral: (%, SegmentBinding %) -> %
integral: (%, Symbol) -> %
li: % -> %

`li(x)` returns the logarithmic integral of `x`, i.e. the integral of `dx / log(x)`.

log: % -> %
pi: () -> %
sec: % -> %
sech: % -> %
Shi: % -> %

`Shi(x)` returns the hyperbolic sine integral of `x`, i.e. the integral of `sinh(x) / x dx`.

Si: % -> %

`Si(x)` returns the sine integral of `x`, i.e. the integral of `sin(x) / x dx`.

sin: % -> %
sinh: % -> %
tan: % -> %
tanh: % -> %

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

ElementaryFunctionCategory

HyperbolicFunctionCategory

PrimitiveFunctionCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory