Basic Functions

abs
abs_symbolic
arg
conjugate

real
real_part
imag
imaginary
imag_part

sqrt

min_symbolic
max_symbolic

sign
sgn

floor
ceil
frac

function
piecewise
spline


Logarithmic Functions

exp
exp_polar
ln
log

harmonic_number

polylog
dilog
lambert_w


Circular Functions

sin
cos
tan
cot
sec
csc

arcsin
asin
arccos
acos

arctan
atan
arctan2
atan2

arccot
acot
arcsec
asec
arccsc
acsc


Hyperbolic Functions

sinh
cosh
tanh
coth
sech
csch

arcsinh
asinh
arccosh
acosh
arctanh
atanh

arccoth
acoth
arcsech
asech
arccsch
acsch


Bessel Functions

bessel_J
bessel_Y
bessel_I
bessel_K

hankel1
hankel2

struve_H
struve_L

spherical_bessel_J
spherical_bessel_Y
spherical_hankel1
spherical_hankel2


Airy Functions

airy_ai
airy_ai_prime
airy_bi
airy_bi_prime


Orthogonal Polynomials

hermite

laguerre
gen_laguerre

legendre_P
legendre_Q
gen_legendre_P
gen_legendre_Q
spherical_harmonic

chebyshev_T
chebyshev_U

jacobi_P
gegenbauer
ultraspherical


Exponential Integrals

exp_integral_ei
Ei
exp_integral_e1
exponential_integral_1
exp_integral_e

log_integral
li
log_integral_offset
Li

sin_integral
Si
cos_integral
Ci

sinh_integral
Shi
cosh_integral
Chi


Elliptic Integrals

elliptic_f
elliptic_kc

elliptic_e
elliptic_ec
elliptic_eu

elliptic_pi


Jacobi Elliptic Functions

jacobi

jacobi_am
jacobi_sn
jacobi_cn
jacobi_dn

jacobi_ns
jacobi_nc
jacobi_nd

jacobi_sc
jacobi_sd
jacobi_cs
jacobi_cd
jacobi_ds
jacobi_dc

inverse_jacobi

inverse_jacobi_sn
inverse_jacobi_cn
inverse_jacobi_dn

inverse_jacobi_ns
inverse_jacobi_nc
inverse_jacobi_nd

inverse_jacobi_sc
inverse_jacobi_sd
inverse_jacobi_cs
inverse_jacobi_cd
inverse_jacobi_ds
inverse_jacobi_cd


Hypergeometric Functions

hypergeometric
hypergeometric_M
hypergeometric_U


Gamma Functions

gamma
factorial
beta
binomial

psi
log_gamma
incomplete_gamma
gamma_inc
gamma_inc_lower

erf
error_fcn


Zeta Functions

zeta
zetaderiv
zeta_symmetric
hurwitz_zeta


Generalized Functions

kronecker_delta
dirac_delta
heaviside
unit_step
spike_function


Miscellaneous Functions

dickman_rho
elliptic_j
legendre_phi
partial_sieve_function
prime_pi

wigner_3j
clebsch_gordan
gaunt
wigner_6j
racah
wigner_9j

sagemath-docs