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from __future__ import absolute_import 

 

from sage.misc.lazy_import import lazy_import 

 

lazy_import('sage.functions.piecewise_old', 'Piecewise') # deprecated 

lazy_import('sage.functions.piecewise', 'piecewise') 

lazy_import('sage.functions.error', ['erf', 'erfc', 'erfi', 'erfinv']) 

 

from .trig import ( sin, cos, sec, csc, cot, tan, 

asin, acos, atan, 

acot, acsc, asec, 

arcsin, arccos, arctan, 

arccot, arccsc, arcsec, 

arctan2, atan2) 

 

from .hyperbolic import ( tanh, sinh, cosh, coth, sech, csch, 

asinh, acosh, atanh, acoth, asech, acsch, 

arcsinh, arccosh, arctanh, arccoth, arcsech, arccsch ) 

 

reciprocal_trig_functions = {'sec': cos, 'csc': sin, 'cot': tan, 'sech': cosh, 'csch': sinh, 'coth': tanh} 

 

 

 

from .other import ( ceil, floor, abs_symbolic, sqrt, 

arg, real_part, real, frac, 

factorial, binomial, 

imag_part, imag, imaginary, conjugate, cases, 

complex_root_of) 

from .log import (exp, exp_polar, log, ln, polylog, dilog, lambert_w, harmonic_number) 

 

 

from .transcendental import (zeta, zetaderiv, zeta_symmetric, hurwitz_zeta, 

dickman_rho, stieltjes) 

 

from .bessel import (bessel_I, bessel_J, bessel_K, bessel_Y, 

Bessel, struve_H, struve_L, hankel1, hankel2, 

spherical_bessel_J, spherical_bessel_Y, 

spherical_hankel1, spherical_hankel2) 

 

from .special import (spherical_harmonic, elliptic_e, 

elliptic_f, elliptic_ec, elliptic_eu, 

elliptic_kc, elliptic_pi, elliptic_j, error_fcn) 

 

from .jacobi import (jacobi, inverse_jacobi, jacobi_nd, jacobi_ns, jacobi_nc, 

jacobi_dn, jacobi_ds, jacobi_dc, jacobi_sn, jacobi_sd, 

jacobi_sc, jacobi_cn, jacobi_cd, jacobi_cs, jacobi_am, 

inverse_jacobi_nd, inverse_jacobi_ns, inverse_jacobi_nc, 

inverse_jacobi_dn, inverse_jacobi_ds, inverse_jacobi_dc, 

inverse_jacobi_sn, inverse_jacobi_sd, inverse_jacobi_sc, 

inverse_jacobi_cn, inverse_jacobi_cd, inverse_jacobi_cs) 

 

from .orthogonal_polys import (chebyshev_T, 

chebyshev_U, 

gen_laguerre, 

gen_legendre_P, 

gen_legendre_Q, 

hermite, 

jacobi_P, 

laguerre, 

legendre_P, 

legendre_Q, 

ultraspherical, 

gegenbauer) 

 

from .spike_function import spike_function 

 

from .prime_pi import legendre_phi, partial_sieve_function, prime_pi 

 

from .wigner import (wigner_3j, clebsch_gordan, racah, wigner_6j, 

wigner_9j, gaunt) 

 

from .generalized import (dirac_delta, heaviside, unit_step, sgn, sign, 

kronecker_delta) 

 

from .min_max import max_symbolic, min_symbolic 

 

from .airy import airy_ai, airy_ai_prime, airy_bi, airy_bi_prime 

 

from .exp_integral import (exp_integral_e, exp_integral_e1, log_integral, li, Li, 

log_integral_offset, 

sin_integral, cos_integral, Si, Ci, 

sinh_integral, cosh_integral, Shi, Chi, 

exponential_integral_1, Ei, exp_integral_ei) 

 

from .hypergeometric import hypergeometric, hypergeometric_M, hypergeometric_U 

 

from .gamma import (gamma, psi, beta, log_gamma, 

gamma_inc, incomplete_gamma, gamma_inc_lower)