LiouvillianFunctionCategory

trigcat.spad line 178 [edit on github]

Category for the transcendental Liouvillian functions.

^: (%, %) -> %

from ElementaryFunctionCategory

acos: % -> %

from ArcTrigonometricFunctionCategory

acosh: % -> %

from ArcHyperbolicFunctionCategory

acot: % -> %

from ArcTrigonometricFunctionCategory

acoth: % -> %

from ArcHyperbolicFunctionCategory

acsc: % -> %

from ArcTrigonometricFunctionCategory

acsch: % -> %

from ArcHyperbolicFunctionCategory

asec: % -> %

from ArcTrigonometricFunctionCategory

asech: % -> %

from ArcHyperbolicFunctionCategory

asin: % -> %

from ArcTrigonometricFunctionCategory

asinh: % -> %

from ArcHyperbolicFunctionCategory

atan: % -> %

from ArcTrigonometricFunctionCategory

atanh: % -> %

from ArcHyperbolicFunctionCategory

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: % -> %

from TrigonometricFunctionCategory

cosh: % -> %

from HyperbolicFunctionCategory

cot: % -> %

from TrigonometricFunctionCategory

coth: % -> %

from HyperbolicFunctionCategory

csc: % -> %

from TrigonometricFunctionCategory

csch: % -> %

from HyperbolicFunctionCategory

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: % -> %

from ElementaryFunctionCategory

fresnelC: % -> %

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

fresnelS: % -> %

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

integral: (%, SegmentBinding %) -> %

from PrimitiveFunctionCategory

integral: (%, Symbol) -> %

from PrimitiveFunctionCategory

li: % -> %

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

log: % -> %

from ElementaryFunctionCategory

pi: () -> %

from TranscendentalFunctionCategory

sec: % -> %

from TrigonometricFunctionCategory

sech: % -> %

from HyperbolicFunctionCategory

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: % -> %

from TrigonometricFunctionCategory

sinh: % -> %

from HyperbolicFunctionCategory

tan: % -> %

from TrigonometricFunctionCategory

tanh: % -> %

from HyperbolicFunctionCategory

ArcHyperbolicFunctionCategory

ArcTrigonometricFunctionCategory

ElementaryFunctionCategory

HyperbolicFunctionCategory

PrimitiveFunctionCategory

TranscendentalFunctionCategory

TrigonometricFunctionCategory