This assumes "x", "y", "z", and "r" are related to formula_1 and formula_2 through the usual spherical-to-Cartesian coordinate transformation::formula_3== Spherical harmonics ===== l = 0===:formula_4=== l = 1 ===:formula_5=== l = 2===:formula_6:formula_7:formula_8:formula_9:formula_10===l = 3===:formula_11:formula_12:formula_13:formula_14:formula_15:formula_16:formula_17=== l = 4===:formula_18:formula_19:formula_20:formula_21:formula_22:formula_23:formula_24:formula_25:formula_26=== l = 5===:formula_27:formula_28:formula_29:formula_30:formula_31:formula_32:formula_33:formula_34:formula_35:formula_36:formula_37=== l = 6===:formula_38:formula_39:formula_40:formula_41:formula_42:formula_43:formula_44:formula_45:formula_46:formula_47:formula_48:formula_49:formula_50=== l = 7===:formula_51:formula_52:formula_53:formula_54:formula_55:formula_56:formula_57:formula_58:formula_59:formula_60:formula_61:formula_62:formula_63:formula_64:formula_65=== l = 8 ===:formula_66:formula_67:formula_68:formula_69:formula_70:formula_71:formula_72:formula_73:formula_74:formula_75:formula_76:formula_77:formula_78:formula_79:formula_80:formula_81:formula_82===l = 9===:formula_83:formula_84:formula_85:formula_86:formula_87:formula_88:formula_89:formula_90:formula_91:formula_92:formula_93:formula_94:formula_95:formula_96:formula_97:formula_98:formula_99:formula_100:formula_101===l = 10===:formula_102:formula_103:formula_104:formula_105:formula_106:formula_107:formula_108:formula_109:formula_110:formula_111:formula_112:formula_113:formula_114:formula_115:formula_116:formula_117:formula_118:formula_119:formula_120:formula_121:formula_122== Real spherical harmonics==For each real spherical harmonic, the corresponding atomic orbital symbol ("s", "p", "d", "f", "g") is reported as well.
Связь между x, y, z, и r, formula_1, formula_2 определяется по следующим образом:: formula_3== Сферические функции с "l" = 0 ==: formula_4=== Вещественные сферические функции с "l" = 0 ===: formula_5== Сферические функции с "l" = 1 ==: formula_6=== Вещественные сферические функции с "l" = 1 ===: formula_7== Сферические функции с "l" = 2 ==: formula_8: formula_9: formula_10: formula_11: formula_12: formula_13: formula_14: formula_15: formula_16: formula_17== Сферические функции с "l" = 3 ==: formula_18: formula_19: formula_20: formula_21: formula_22: formula_23: formula_24: formula_25: formula_26: formula_27: formula_28: formula_29: formula_30: formula_31== Сферические функции с "l" = 4 ==: formula_32: formula_33: formula_34: formula_35: formula_36: formula_37: formula_38: formula_39: formula_40: formula_41: formula_42: formula_43: formula_44: formula_45: formula_46: formula_47: formula_48: formula_49== Сферические функции с "l" = 5 ==: formula_50: formula_51: formula_52: formula_53: formula_54: formula_55: formula_56: formula_57: formula_58: formula_59: formula_60== Сферические функции с "l" = 6 ==: formula_61: formula_62: formula_63: formula_64: formula_65: formula_66: formula_67: formula_68: formula_69: formula_70: formula_71: formula_72: formula_73== Сферические функции с "l" = 7 ==: formula_74: formula_75: formula_76: formula_77: formula_78: formula_79: formula_80: formula_81: formula_82: formula_83: formula_84: formula_85: formula_86: formula_87: formula_88== Сферические функции с "l" = 8 ==: formula_89: formula_90: formula_91: formula_92: formula_93: formula_94: formula_95: formula_96: formula_97: formula_98: formula_99: formula_100: formula_101: formula_102: formula_103: formula_104: formula_105== Сферические функции с "l" = 9 ==: formula_106: formula_107: formula_108: formula_109: formula_110: formula_111: formula_112: formula_113: formula_114: formula_115: formula_116: formula_117: formula_118: formula_119: formula_120: formula_121: formula_122: formula_123: formula_124== Сферические функции с "l" = 10 ==: formula_125: formula_126: formula_127: formula_128: formula_129: formula_130: formula_131: formula_132: formula_133: formula_134: formula_135: formula_136: formula_137: formula_138: formula_139: formula_140: formula_141: formula_142: formula_143: formula_144: formula_145== См.