1Special 2======= 3 4DiracDelta 5---------- 6.. autoclass:: sympy.functions.special.delta_functions.DiracDelta 7 :members: 8 9Heaviside 10--------- 11.. autoclass:: sympy.functions.special.delta_functions.Heaviside 12 :members: 13 14Singularity Function 15-------------------- 16.. module:: sympy.functions.special.singularity_functions 17 18.. autoclass:: sympy.functions.special.singularity_functions.SingularityFunction 19 :members: 20 21Gamma, Beta and related Functions 22--------------------------------- 23.. module:: sympy.functions.special.gamma_functions 24 25.. autoclass:: sympy.functions.special.gamma_functions.gamma 26 :members: 27.. autoclass:: sympy.functions.special.gamma_functions.loggamma 28 :members: 29.. autoclass:: sympy.functions.special.gamma_functions.polygamma 30 :members: 31.. autoclass:: sympy.functions.special.gamma_functions.digamma 32 :members: 33.. autoclass:: sympy.functions.special.gamma_functions.trigamma 34 :members: 35.. autoclass:: sympy.functions.special.gamma_functions.uppergamma 36 :members: 37.. autoclass:: sympy.functions.special.gamma_functions.lowergamma 38 :members: 39.. autoclass:: sympy.functions.special.gamma_functions.multigamma 40 :members: 41.. module:: sympy.functions.special.beta_functions 42.. autoclass:: sympy.functions.special.beta_functions.beta 43 :members: 44 45Error Functions and Fresnel Integrals 46------------------------------------- 47.. module:: sympy.functions.special.error_functions 48 49.. autoclass:: sympy.functions.special.error_functions.erf 50 :members: 51.. autoclass:: sympy.functions.special.error_functions.erfc 52 :members: 53.. autoclass:: sympy.functions.special.error_functions.erfi 54 :members: 55.. autoclass:: sympy.functions.special.error_functions.erf2 56 :members: 57.. autoclass:: sympy.functions.special.error_functions.erfinv 58 :members: 59.. autoclass:: sympy.functions.special.error_functions.erfcinv 60 :members: 61.. autoclass:: sympy.functions.special.error_functions.erf2inv 62 :members: 63 64.. autoclass:: sympy.functions.special.error_functions.FresnelIntegral 65 :members: 66 67.. autoclass:: fresnels 68 :members: 69.. autoclass:: fresnelc 70 :members: 71 72Exponential, Logarithmic and Trigonometric Integrals 73---------------------------------------------------- 74 75.. autoclass:: Ei 76 :members: 77.. autoclass:: expint 78 :members: 79.. autofunction:: E1 80.. autoclass:: li 81 :members: 82.. autoclass:: Li 83 :members: 84.. autoclass:: Si 85 :members: 86.. autoclass:: Ci 87 :members: 88.. autoclass:: Shi 89 :members: 90.. autoclass:: Chi 91 :members: 92 93Bessel Type Functions 94--------------------- 95 96.. module:: sympy.functions.special.bessel 97 98.. autoclass:: sympy.functions.special.bessel.BesselBase 99 :members: 100 101.. autoclass:: sympy.functions.special.bessel.besselj 102 :members: 103.. autoclass:: sympy.functions.special.bessel.bessely 104 :members: 105.. _besseli: 106.. autoclass:: sympy.functions.special.bessel.besseli 107 :members: 108.. autoclass:: sympy.functions.special.bessel.besselk 109 :members: 110.. autoclass:: sympy.functions.special.bessel.hankel1 111 :members: 112.. autoclass:: sympy.functions.special.bessel.hankel2 113 :members: 114.. autoclass:: sympy.functions.special.bessel.jn 115 :members: 116.. autoclass:: sympy.functions.special.bessel.yn 117 :members: 118 119.. autofunction:: sympy.functions.special.bessel.jn_zeros 120 121.. autoclass:: sympy.functions.special.bessel.marcumq 122 :members: 123 124Airy Functions 125-------------- 126 127.. autoclass:: sympy.functions.special.bessel.AiryBase 128 :members: 129 130.. autoclass:: sympy.functions.special.bessel.airyai 131 :members: 132.. autoclass:: sympy.functions.special.bessel.airybi 133 :members: 134.. autoclass:: sympy.functions.special.bessel.airyaiprime 135 :members: 136.. autoclass:: sympy.functions.special.bessel.airybiprime 137 :members: 138 139B-Splines 140--------- 141 142.. autofunction:: sympy.functions.special.bsplines.bspline_basis 143.. autofunction:: sympy.functions.special.bsplines.bspline_basis_set 144.. autofunction:: sympy.functions.special.bsplines.interpolating_spline 145 146Riemann Zeta and Related Functions 147---------------------------------- 148.. module:: sympy.functions.special.zeta_functions 149 150.. autoclass:: zeta 151 :members: 152.. autoclass:: dirichlet_eta 153 :members: 154.. autoclass:: polylog 155 :members: 156.. autoclass:: lerchphi 157 :members: 158.. autoclass:: stieltjes 159 :members: 160 161Hypergeometric Functions 162------------------------ 163.. autoclass:: sympy.functions.special.hyper.hyper 164 :members: 165 166.. autoclass:: sympy.functions.special.hyper.meijerg 167 :members: 168 169.. autoclass:: sympy.functions.special.hyper.appellf1 170 :members: 171 172Elliptic integrals 173------------------ 174.. module:: sympy.functions.special.elliptic_integrals 175 176.. autoclass:: elliptic_k 177 :members: 178.. autoclass:: elliptic_f 179 :members: 180.. autoclass:: elliptic_e 181 :members: 182.. autoclass:: elliptic_pi 183 :members: 184 185Mathieu Functions 186----------------- 187.. module:: sympy.functions.special.mathieu_functions 188 189.. autoclass:: sympy.functions.special.mathieu_functions.MathieuBase 190 :members: 191 192.. autoclass:: sympy.functions.special.mathieu_functions.mathieus 193 :members: 194.. autoclass:: sympy.functions.special.mathieu_functions.mathieuc 195 :members: 196.. autoclass:: sympy.functions.special.mathieu_functions.mathieusprime 197 :members: 198.. autoclass:: sympy.functions.special.mathieu_functions.mathieucprime 199 :members: 200 201Orthogonal Polynomials 202---------------------- 203 204.. automodule:: sympy.functions.special.polynomials 205 206Jacobi Polynomials 207++++++++++++++++++ 208 209.. autoclass:: sympy.functions.special.polynomials.jacobi 210 :members: 211 212.. autofunction:: sympy.functions.special.polynomials.jacobi_normalized 213 214Gegenbauer Polynomials 215++++++++++++++++++++++ 216 217.. autoclass:: sympy.functions.special.polynomials.gegenbauer 218 :members: 219 220Chebyshev Polynomials 221+++++++++++++++++++++ 222 223.. autoclass:: sympy.functions.special.polynomials.chebyshevt 224 :members: 225 226.. autoclass:: sympy.functions.special.polynomials.chebyshevu 227 :members: 228 229.. autoclass:: sympy.functions.special.polynomials.chebyshevt_root 230 :members: 231 232.. autoclass:: sympy.functions.special.polynomials.chebyshevu_root 233 :members: 234 235Legendre Polynomials 236++++++++++++++++++++ 237 238.. autoclass:: sympy.functions.special.polynomials.legendre 239 :members: 240 241.. autoclass:: sympy.functions.special.polynomials.assoc_legendre 242 :members: 243 244Hermite Polynomials 245+++++++++++++++++++ 246 247.. autoclass:: sympy.functions.special.polynomials.hermite 248 :members: 249 250Laguerre Polynomials 251++++++++++++++++++++ 252 253.. autoclass:: sympy.functions.special.polynomials.laguerre 254 :members: 255.. autoclass:: sympy.functions.special.polynomials.assoc_laguerre 256 :members: 257 258Spherical Harmonics 259------------------- 260 261.. autoclass:: sympy.functions.special.spherical_harmonics.Ynm 262 :members: 263 264.. autofunction:: sympy.functions.special.spherical_harmonics.Ynm_c 265 266.. autoclass:: sympy.functions.special.spherical_harmonics.Znm 267 :members: 268 269Tensor Functions 270---------------- 271 272.. autofunction:: sympy.functions.special.tensor_functions.Eijk 273 274.. autofunction:: sympy.functions.special.tensor_functions.eval_levicivita 275 276.. autoclass:: sympy.functions.special.tensor_functions.LeviCivita 277 :members: 278 279.. autoclass:: sympy.functions.special.tensor_functions.KroneckerDelta 280 :members: 281