Function Encyclopedia

imm(a,b)

impliesc(a,b)

impliesr(a, b)

lerp(a, b, t)

sources:W

magnetj1(a, b=a,n=1)

magnetj2(a, b=a,n=1)

realgeneralizedalgebraicsmoothstep(x,k=2)

sources:W

realsmoothtransition(x,m=1)

rehab(P)

relu(x)

sources:W

reluc(x)

sources:W

remp(A, B)

reversebesselpoly(n,x)

sources:X D

reversesuperstar(b)

rexa(x,k,s,z=0)

sources:X

rexcS(x,S)

rexhcS(x,S)

rexoid(x,y,e=0)

rexp(x)

rexxy(x,y,s,e=0)

multicoloredsun(t,s=1,e=0)

multicoloredsunx(t,s=1,e=0)

multicoloredsuny(t,s=1,e=0)

multifacti(x, a)

multifactiauxilary(x, m, a)

multilinearpolynomial(M,X)

sources:W

multilinearrectangular(M,A,B,X)

sources:W

multilinearrectangularvertices(M,A,B,X)

sources:W

multimagic(n,k)

sources:O

multipleholdersin(x,A)

sources:X X

multiplesin(x,A)

sources:X

multipowerbrot(a, b=a,m=2,n=1)

multiqpochhammer(A,q,n)

multiscroll(e,XYZ=[0.1,0.3,-0.6],a=36,b=3,c=20,u=-15.15,N=bign)

sources:W

multiset(n,r)

multivariablebeta(A)

expaexp(x,q,a)

expbump(x)

sources:W

expbump2(x,c=-1,d=1)

sources:W

expmsqr(b)

expo(func,a,b,x)

expolocate(x)

exponentialbellpoly(n,k,X)

exponentialexpectedshprtfall(l)

exponentialfisherinfo(l)

sources:N

exponentialfisherkullbackleiblerdiv(l0,l)

exponentialintegrator(e,s=0,L=0,N= ,steps=bign)

sources:W

exponentialpoly(A,n,z)

exponentialpowerexcessentropy(m,a,b)

sources:N

exponentialpowerskew(m,a,b)

sources:N

exponentialskew(l)

sources:N

exponentialwindow(x, nn, tau)

sources:W

expp(x)

lncos(x,n=1)

lncot(x,n=1)

lncsc(x,n=1)

lnsec(x,n=1)

lnsin(x,n=1)

lntan(x,n=1)

logarithmicscore(P,i)

sources:W

logfouriertransform(f,k,p=0,N=bign,xMax=sqrt(bign)

crd(b)

crdv(x)

sphericalkdv(x,t,u0,off=0,N=bign)

sphericalkdvcoeffdiff(a,t)

spheroconalsc(n,m,b,c,kk)

sources:X

spheroconalss(n,m,b,c,kk)

sources:X

vercosin(b)

xmsin(x)

arcxpsin(x)

dtanpi4pcos(x,d=1)

riesel(k,n)

stellayen(x)

bent(n)

continuousdivisorgenerating(q,a)

degeneratebernoullid(t,n,l)

sources:X

degeneratebernoullinum(n,l,a=1e-5)

sources:X

degenerateeulerd(t,n,l)

sources:X

degenerateeulernum(n,l,a=1e-5)

sources:X

entringerpouperdgeneratingdelta(x,y)

sources:X

entringerpouperdgeneratingupsilon(x,y,z)

sources:X

eulertricomigeneral(x,y,k,p=0,q=0)

sources:W E

generalizedbernoullinum(v,n,b)

sources:D W

generalizedbernoullinuml(n,l,a=0)

sources:X D W

generalizedeulernumc(a,n)

sources:X

generalizedeulernumcc(a,n)

sources:X

generalizedeulernumcd(a,n)

sources:X

generalizedeulernumd(a,n)

sources:X

generalizedeulernuml(n,l,a=0)

sources:X

generalizedpolynomialsintuple(A,l,j)

generalizedruler(n, p)

generalizedscollatz(n,k)

sources:O O

generalizedtribonacci(x,a=1,b=0,c=1,r=1,s=1,t=1)

sources:

unificationgeneratingfunction(v,x,t,k,a,b,bb)

sources:X

unificationgeneratingfunction2(t,Q)

sources:X

whitneyrankgeneratingfunction(a,x,y)

aperynumber(k)

sources:S

apostalbernoullinum(v,n,b)

sources:D W

apostalbernoullipoly(v,n,x,b)

sources:D W

hqtwistedbernoullinum(h,n,z,q)

sources:D W

riemann(x)

riemannj(x)

riemannlinear(x,t,rhol,ul,rhor,ur,rho0,a)

sources:W

riemannp(a,b,c,al,bl,cl,ap,bp,cp,z)

sources:W V

riemannproblem(x,t,ul,ur,f,xmin,xmax,nx,dt,nt)

sources:W

idealizebasis(A)

alternatingfactorialuu(x)

modulardiscriminant(t)

sources:W V D W

modulardiscriminantq(q)

sources:W V D W

heckedoublesum(a,b,c,x,y,q)

sources:X

generalizedramanujantau(n,k)

minkowskiquestionmarkgeneralized(x,n=3)

sources:W

incgeneralizedharmonicnum(n,q,s)

caputof(t,...x)

sources:X

caputog(t,...x)

caputoh(t,...x)

sources:X

estimatefractionalbrownian(func, { samples = 2048, hs = [1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128] } = {})

estimatefractionalbrownianexponent(func, { samples = 2048, hs = [1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128] } = {})

fractionalbrownian(t, H = 0.5, reset = 0)

fractionalfouriertransform(f,a,p=0,N=bign,xMax=sqrt(bign)

sources:W

fractionalintg(func,input,mk,a=0)

fractionalisprime(x)

fractionalorderbenjaminbonamahonykadomtsevpetviashviliauxiliary(x,y,z,t,alpha,m1,m2,m3,w1,w3,b1,b2)

fractionalorderbenjaminbonamahonykadomtsevpetviashviliintegrator(x,y,z,t,alpha,w1,w2,w3,b1,b2,n,u0,xmin=-5,xmax=5,ymin=-5,ymax=5,zmin=-5,zmax=5,M=20,K=20,L=20,N=bign)

fractionalorderbenjaminbonamahonykadomtsevpetviashviliphase(x,y,z,t,alpha,m1,m2,m3,w1,w3,b1,b2)

sources:X

fractionalorderbenjaminbonamahonykadomtsevpetviashvilitravelingwave(x,y,z,t,alpha,m1,m2,m3,c)

sources:X

fractionalsequence(A,x)

fractionalsequences(A,x)

lagder(f,x)

ampquadratic(x,a=-1,b=0,c=1,parity=0)

berndtintegral(s,m)

sources:X X W X

berndtintegrald(x,Q)

sources:X X W X

berndtmintegral(s,m)

sources:X

berndtmintegrald(x,Q)

sources:W X

biquadratic(b)

bournezpoulypwcgenintegral(t,y0,q,phi=20,N=bign)

bournezpoulyreachintegral(t,y0,g,phi=1,N=bign)

sources:X

canonicalintegral(A)

sources:D

canonicalintegrald(t,A)

sources:D

catalanintegral(z,y)

sources:O O

catalanintegral2(z,y)

sources:O

chandrasekharvirialintegrate(func,X)

sources:W

cintegral(func, C, t = 0, N = bign)

cintegraltest(x)

cquadraticmean(func,a,b)

cquadraticmeanfunc(func,a,b)

dampedexponentialcosineintegral(t,tt)

sources:X

djlintegrate(x0,x1,z0,z1,nx,nz,y,U,Up,N,c,steps)

djlintegratesimple(x0,x1,z0,z1,nx,nz,y,N,c,steps)

dyonsintegral(n,b)

generalizedquadraticsin(a,b,c,l,x)

hyoerpolicquadraticcylinderx(t,s,n=4,m=1,e=0)

hyoerpolicquadraticcylindery(t,s,n=4,m=1,e=0)

incompletedampedexponentialcosineintegral(t,tt,x)

sources:X

integral(func, initial, end, input, N = bign)

integrala(func, initial, end, input, N = bign)

integraladaptive(func, a, b, input, tol = 1e-10, maxDepth = 0)

integraladaptivecomplex(func, a, b, input, steps = bign,N=bign)

integraladaptives(func, a, b, input, tol = 1e-3)

integralclenshawcurtis(func, initial, end, input, N = bign)

integralgauss(func, initial, end, input, N = bign)

integralold(func, initial, end, input, N = bign)

integraltanhsinh(func, initial, end, input, N = bign)

integraltanhsinhf(func, initial, end, input, N = bign)

integraltanhsinhg(func, initial, end, input, tol = 0.00001/bign/bign, maxDepth = bign, h = 0.25)

integrateadams(profilefunc,step=bign)

sources:W

kernelexpquadratic(u)

kernelinversequad(u)

kernelquadratic(u)

kernelquadraticinverse(u)

lfuncquad(a,s)

sources:X

ndquadratic(x1,x2)

primitiveequations(u,v,t,w,p,dx,dy,dt,f,R,cp)

sources:W

primitiveequationsintegrator(u,v,t,w,p,dx,dy,dt,f,R,cp,n)

sources:W

productintegralbigeometric(f,a,b,N=bign)

sources:W

productintegralgeometric(f,a,b,N=bign)

sources:W

productintegralvolterra(f,a,b,N=bign)

sources:W

qintegral2(func,x,q,p)

quadraticbinarymodular(a,b,c,q)

quadraticdiscriminant(a,b,c)

quadraticrepresentation(Q,n)

quadraticscore(P,i=0)

sources:W

quadraticsequencemean(args)

quadratictwistcurve(x,d=1,a2=2,a4=3,a6=4,parity=0)

quadrilobeelasticforcex(x,w,k)

quadrilobeelasticforcey(x,w,k)

quadripod(x,y)

quadruple(x)

radialinvmultiquadratic(s,x)

sources:W

radialmultiquadratic(s,x)

sources:W

selbergintegral(n,c)

solvequadratic(a, b, c=0, parity = 0)

superquadratic(x,a=2,b=0,c=0,ri=1,bignc=bign*1,parityfix=1,parityinv=parityfix)

wallisintegral(n)

wallisintegrald(t,n)

converse(a, b)

toronto(m,n,r)

walker(n)

sources:X

walkerd(x)

sources:X

selbergdelta(A)

floquet(P,Q,z,s=1,sp=0,per=Math.PI,h=per/bign)

gequation(x,sl,u,c=1)

gequationang(x,sl,t,c=1)

gequationeq(x,y,t,g0,velocity,st=1,N=bign,h=0.001)

gequationlocal(x,y,t,g0,velocity,st=1,N=bign,h=0.001)

linanequation(y,v,delta,gamma,z0,z1,n=bign)

sources:W W

quartictransform(f,k,p=0,N=bign,xMax=sqrt(bign)

tridiageig(A)

transposea(A)

associateEigenvectors(matrix, eigenvalues, eigenvectors)

findEigenvectors(matrix, tolerance = 1e-10, maxIterations = 100)

findEigenvectorst(matrix,tolerance=1e-10,maxIterations=1000)

eigenvals(A,maxIter=1000,tol=1e-12)

eigenvalsold(A, maxIter = 1000, tol = 1e-12)

eigenvecs(A,vals=eigenvals(A)

eigenvecsold(A,a, maxIter = 1000, tol = 1e-10)

dominanteigenvalue(A, iters = 1000)

dominanteigenvector(A, iters = 1000)

dominanteigenvectorindex(A)

dominanteigenvectorvalue(A)

dominoschur(L,X)

dominoshiftedschur(L,n,X)

principaldominoschur(L,n,x)

principalshifteddominoschur(L,n,x)

principalschurpoly(L,x)

principalshiftedschurpoly(lambda, x)

schurpoly(L,X)

shiftedschurpoly(lambda, X)

quotientschur(L,n,X)

supersymmetricschurpoly(lambda, X, Y)

principalsupersymmetricschurpoly(L,x, y)

hilleigenfunction(x,a=[],b=[],lambda=0,N=bign)

johnsonschemeeigenp(n,l,i,k)

johnsonschemeeigenq(n,l,i,k)

macdonaldeigenvalueb(M,q,t)

sources:X

tridiagonalmatrix(U, M, D)

arcfermat(b)

fermat(b)

sources:V

halffermat(x,a=0.5)

jordanpolya(A)

jordantotient(n, k = 1)

sources:

semifermat(x)

superfermat(x,a=-1,N=bign+1)

Ccircle(r=1, x=math.complex(0,0)

circle(x,p=1,parity=0)

sources:V

circlehaystackx(t,s,e=pi()

circlehaystacky(t,s,e=0)

hyperspherevolume(n,r=1)

kleingordon(xmin,xmax,ymin,ymax,nx,ny,phi0,dphi0,m,c,hbar,J,dt,steps,x,y)

sources:W E

kleinquartic(x,y,parity=1)

kleinquartic2(x,y,z)

metricsphere(r)

oseenmovingspherepsi(r,theta,U,a,R)

sources:W

oseenmovingspherevelocity(r,theta,U,a,R,h)

sources:W

sdicircle(x,y,r)

sumsquaresonsphere(a, b)

superintegrableschrodingerfreesphere(x,l,m,E=0,c1=1,c2=0)

selectorcircle(z)

sources:W

stereopdisdyakisdodecahedron(x,a=0,h=2)

sources:W

stereopdodecahedron(x,a=0,h=2)

stereopentakisdodecahedron(x, a=0,h=2)

sources:W

stereopicosahedron(x,a=0,h=2)

sources:W

stereopicosidodecahedron(x,a=0,h=2)

stereoppentakisdodecahedron(x,a=0,h=2)

sources:W

stereoprhombicdodecahedron(x,a=0,h=2)

sources:W

stereoprhombicosidodecahedron(x,a=0,h=2)

sources:W

stereopsnubdodecahedron(x,a=0,h=2)

stereoptetrakishexahedron(x,a=0,h=2)

sources:W

stereoptruncateddodecahedron(x,a=0,h=2)

stereoptruncatedicosidodecahedron(x,a=0,h=2)

stereopdihedron(x,n=5,a=0,h=2)

sources:W

stereopdisdyakistriacontahedron(x,a=0,h=2)

stereopdjhonson(n, x, a = 0, rot = [0, 0, 0], trans = [0, 0, 0], h = 2)

stereophosohedron(x,n=5,a=0,h=2)

stereopjhonson(n, x, a = 0, rot = [0, 0, 0], trans = [0, 0, 0], h = 2)

stereoppseudodihedron(z,l=5,a=0)

stereoppseudoholohedron(z,l=5,a=0)

stereoproject(Ch, S = , h = 0, a = 2,type= ,repeat=0)

stereoproject2(C, S = , n = 5, h = 0, a = 2,type=)

stereoprojectd(Ch, S = , h = 0, a = 2, type = , l = 1, rot = [0, 0, 0], trans = [0, 0, 0], autofix = 0)

stereoprojectdraw(C, S = , h = 0, a = 2, type = , l = 1, rot = [0, 0, 0], trans = [0, 0, 0], autofix = 0)

stereoprojectraw(C, S = , h = 0, a = 2,type= ,repeat=0)

stereopseudodihedron(z,l=5)

stereopseudoholohedron(z,l=5)

stereopszilassi(x,a=0,h=2)

sources:W

stereopdeltoidalicositetrahedron(x,a=0,h=2)

sources:W

stereopentagonalhexecontahedron(x, a=0,h=2)

sources:W

stereopentagonalicositetrahedron(x, a=0,h=2)

sources:W

stereoppentagonalhexecontahedron(x,a=0,h=2)

sources:W

stereoppentagonalicositetrahedron(x,a=0,h=2)

sources:W

stereoptetrahedron(x, a=0,h=2)

sources:W

stereoptriakistetrahedron(x,a=0,h=2)

sources:W

stereoptruncatedtetrahedron(x,a=0,h=2)

sources:W

stereopdeltoidalhexecontahedron(x,a=0,h=2)

sources:W

stereopcube(x,a=0,h=2)

sources:W

stereopcuboctahedron(x,a=0,h=2)

stereopgreatcube(x, a=0,h=2)

sources:W

stereopoctahedron(x,a=0,h=2)

sources:W

stereoprhombicuboctahedron(x,a=0,h=2)

sources:W

stereopsnubcube(x,a=0,h=2)

stereopstellaoctangula(x,a=0,h=2)

stereopstellatedcube(x, a=0,h=2)

sources:W

stereoptriakisicosahedron(x,a=0,h=2)

sources:W

stereoptriakisoctahedron(x,a=0,h=2)

sources:W

stereoptruncatedcube(x,a=0,h=2)

stereoptruncatedcuboctahedron(x,a=0,h=2)

sources:W

stereoptruncatedicosahedron(x,a=0,h=2)

sources:W

stereoptruncatedoctahedron(x,a=0,h=2)

sources:W

stereoprhombictriacontahedron(x,a=0,h=2)

sources:W

conjconwaypolsmy(sm,t)

sources:W

conjconwaypoly(b,t)

sources:O

reducedburau(b,t)

sources:O

reducedburaurepresentation(braid, t)

sources:W

reshetikhinturaevinvariant(r,A,B,D,Q)

alexandermatrix(b,t)

alexandermatrixsm(sm,t)

sources:W O

alexanderpoly(b,t)

sources:W O

alexanderpolysm(sm,t)

sources:W O

unnormalizedalexander(b,t)

sources:W O

unnormalizedalexanderpolysm(sm,t)

sources:W O

conwaypoly(b,t)

hauysquarepyramid(b)

oddsquare(X)

randsquare(n)

selectorsquare(z)

setsquaregrid(n)

snubsquarelsec(x,s=0)

sqlatticetan(x,d=0.5)

sqlatticetansqr(x,d=0.5,dd=0.5)

sqqlatticetan(x,d=0.5,dd=0.5)

squarederror(x,y)

squarelsec(x,s=0)

squareltan(x,s=0)

squaremod(x, ll=1.76663875)

squaremodc(x,ll)

squareplus(a,x)

sources:W

squarerolling(x,g=1)

squaresr(d,n)

sources:M N

squarewell(r,V0,R)

squircle(x,n=3,parity=0)

truncsquarelsec(x,s=0)

abcparticlefilter(particles,f,simulate,z,distance,epsilon,noise=noise)

sources:W

approxconfinedgaussianwindow(x, nn, sigma_t)

sources:W

archilbert(b)

auxiliaryparticlefilter(particles,weights,f,predict,likelihood,z,noise=noise)

sources:W

bartletthannwindow(x, nn)

sources:W

bartlettwindow(x, nn)

sources:W

blackmanharriswindow(x, nn)

sources:W

blackmannuttallwindow(x, nn)

sources:W

blackmanwindow(x, nn)

sources:W

bluenoise(x)

brownnoise(x)

chirp(t, f0, f1)

chirptransform(f,k,p=0,N=bign,xMax=sqrt(bign)

confinedgaussianwindow(x, nn, sigma_t)

sources:W

directparticlefilter(particles,f,likelihood,z,noise=noise)

sources:W

feynmanKacparticlefilter(paths,f,G,z,noise=noise)

sources:W

gaussianparticlefilter(particles,f,likelihood,z,sigma,noise=noise)

sources:W

gaussianwindow(x, nn, sigma)

sources:W

gaussnoise(x)

sources:W

generalizedfiltering(state,measurement,generative,observation,steps=1,dt=1,e=0.00001)

sources:W

generalizednormalwindow(x, nn, sigma, p)

sources:W

greynoise(x)

halfhilbert(x,a=0.5)

hammingwindow(x, nn)

sources:W

hannpoissonwindow(x, nn, alpha)

sources:W

hannwindow(x, nn)

sources:W

hierarchicalparticlefilter(groups,f,likelihood,z,noise=noise)

sources:W

hilbert(t,N=floor(sqrt(bign)

kjartanssonattenuation(w,w0,q0,c0)

kolskyattenuation(w,wr,qr,cr)

sources:W

lanczoswindow(x, nn)

sources:W

noise(x)

noiser(t, A0=440, A=1, df=0, min=20, max=20000, maxA=false)

nudgedparticlefilter(particles,f,nudge,likelihood,z,eta,noise=noise)

sources:W

nuttallwindow(x, nn)

sources:W

particlefilter(particles,f,likelihood,z,noise=noise,resample=true)

sources:W

parzenwindow(x, nn)

sources:W

pinknoise(x)

plancktaperwindow(x, nn, epsilon)

sources:W

raoblackwellizedparticlefilter(particles,f,kalmanstep,likelihood,z,noise=noise)

sources:W

signalobservationfilter(particles,transition,observation,z,noise=noise)

slepianwindow(x, nn, alpha)

sources:W

slsattenuation(w,taur,c0,qc)

superhilbert(x,a=1,N=bign)

triangularwindow(x, nn)

sources:W

tukeywindow(x, nn, alpha)

sources:W

unscentedparticlefilter(particles,proposal,likelihood,z,noise=noise)

sources:W

violetnoise(x)

welchwindow(x, nn)

sources:W

rectangularwindow(x, nn)

sources:W

recursiveleastsquaresfilter(state,covariance,x,d,lambda=0.99)

sources:W

Custom Function

imm(a,b)

impliesc(a,b)

impliesr(a, b)

lerp(a, b, t)

magnetj1(a, b=a,n=1)

magnetj2(a, b=a,n=1)

realgeneralizedalgebraicsmoothstep(x,k=2)

realsmoothtransition(x,m=1)

rehab(P)

relu(x)

reluc(x)

remp(A, B)

reversebesselpoly(n,x)

reversesuperstar(b)

rexa(x,k,s,z=0)

rexcS(x,S)

rexhcS(x,S)

rexoid(x,y,e=0)

rexp(x)

rexxy(x,y,s,e=0)

add(...args)

addp(A, B)

addvec(x, idx, eps)

conj(value)

cross3(x1,y1,z1, x2,y2,z2)

cross3v(a,b)

crossc(a, b)

div(...args)

divp(A, B)

dot(v1, v2)

dot2(x1,y1,x2,y2)

dot3(x1,y1,z1,x2,y2,z1)

dot3v(a,b)

dotc(a, b)

hypot(a, b)

hypoth(a, b)

im(b)

IM(b)

mag(b)

mul(...args)

mul3v(a,s)

mulp(A, B)

neg(a)

norm3v(a)

normSqr(z)

re(b)

RE(b)

sub(...args)

sub3v(a,b)

subp(A, B)

subvec(x, idx, eps)

invbump(x)

invei(x)

inveip(n,x)

invexpbeta(w,beta=1)

invflatf(x)

invgudermann(b)

invnegboxcox(x,l)

involutionstanleysymmetric(W,X)

invpower(r,C,n)

invsmoothstep(x)

invsmoothtrans(x)

inversearray(A)

inversecontinued(x)

inversecubic(a, b, c, d = 0, y = 0, parity = 1)

inversedepressedcubic(p,q,k=0)

inversedepressedcubicreal(p,q)

inverseeq(f,x,guess=0)

inverselinear(a, b=0,y=0)

inversemetric(metric, x)

inversequadratic(a, b, c=0,y=0, parity = 0)

inversequartic(a, b, c, d, e = 0, y22 = 0, parity = 0)

inversetriangular(x)

invqamplitude(U,w,t,q,wr)

invqfamplitude(w,t,q,wr)

invqgain(w,t,q,wr)

invqgainclip(w,t,q,wr,maxgain=1e6)

invqgainlowpass(w,t,q,wr,fc,order=4)

invqkolsky(U,w,t,q,wr,cr)