LiouvillianFunctionCategory

trigcat.spad line 178 [edit on github]

Category for the transcendental Liouvillian functions.

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.

Ei : % -> %

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

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.

^ : (%, %) -> %

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

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.

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

sin : % -> %

from TrigonometricFunctionCategory

sinh : % -> %

from HyperbolicFunctionCategory

tan : % -> %

from TrigonometricFunctionCategory

tanh : % -> %

from HyperbolicFunctionCategory

HyperbolicFunctionCategory

ElementaryFunctionCategory

TrigonometricFunctionCategory

TranscendentalFunctionCategory

ArcTrigonometricFunctionCategory

ArcHyperbolicFunctionCategory

PrimitiveFunctionCategory