278
Index
roots, 221
second kind, 216
shifted, 218
third kind, 216
trigonometric representation, 216
Chebyx, 215
Chebyzero, 215, 223
Christoffel-Darboux relation, 184
ClassWeier, 157
Clebsch-Gordan coefficient, 251, 253, 255
Cn, 132
Coherent state, 204
Cohstates, 200, 205
Cohstates_animation, 200
Cone2c, 259, 273
Confluent hypergeometric function, 91, 92
1 F 1 , 92
U, 94
Confluent hypergeometric limit function, 96
Conhyp, 92
Conical function, 34, 51
1st kind, 52
2nd kind, 54
Coordinates
Cartesian, 260
cone, 266
cylindrical, 263
ellipsoidal, 265
elliptic, 267, 269
elliptic cylindrical, 165, 264
hyperspherical, 268
Jacobi, 267
oblate spheroidal, 265
parabolic, 263
parabolic cylindrical, 265
paraboloidal, 265
polar, 267
prolate spheroidal, 264
semiparabolic, 266
spherical, 261
CoordTrafo, 259, 269
Cornu spiral, 31
Cos-integral, 13
Coulomb phase shift, 103
Coulombscatt, 103
Coulomb scattering amplitude, 111
Coulombwave, 103
Coulomb wave function, 101, 105
F l , 103
f l , 104
G l , 104
H
±
l , 103
h l , 104
parabolic coordinates, 102
partial wave, 102
spherical coordinates, 102, 103
Cs, 132
C2hyper, 259, 275
Cylinder functions, 71
D
DawsonC, 23, 28
Dawson integral, 23, 27
Dc, 132
DedeEta, 123, 128
Dedekind η function, 123, 128
Dedekind sum, 127
DHexample.m, 243
Digamma function, 2, 7
DiincgammaC, 2, 11
Discriminant, 153
Dn, 132
Ds, 132
E
Edal2c, 272
Eiga, 166, 177
Eigb, 166, 177
EllipFun, 132, 135
EllipInt, 139, 149
EllipIntQuadtest.m, 150
Ellipj, 132
Ellipke, 139
Elliptic functions, 131
Elliptic integral
Bulirsch, 140
Carlson, 140
cel, 140, 149
D, 139, 142
E, 139, 141
el1, 140, 148
el2, 140, 148
el3, 140, 148
F, 139, 140
first kind, 131, 139
K, 139, 140
Π , 139, 141
RC, 140, 142
RD, 140
RF, 140, 143
RG, 140, 144
RJ, 140
second kind, 139
third kind, 139, 141
Elliptic modular function, 153, 155
ElliptIntQuadTest, 140
Index
roots, 221
second kind, 216
shifted, 218
third kind, 216
trigonometric representation, 216
Chebyx, 215
Chebyzero, 215, 223
Christoffel-Darboux relation, 184
ClassWeier, 157
Clebsch-Gordan coefficient, 251, 253, 255
Cn, 132
Coherent state, 204
Cohstates, 200, 205
Cohstates_animation, 200
Cone2c, 259, 273
Confluent hypergeometric function, 91, 92
1 F 1 , 92
U, 94
Confluent hypergeometric limit function, 96
Conhyp, 92
Conical function, 34, 51
1st kind, 52
2nd kind, 54
Coordinates
Cartesian, 260
cone, 266
cylindrical, 263
ellipsoidal, 265
elliptic, 267, 269
elliptic cylindrical, 165, 264
hyperspherical, 268
Jacobi, 267
oblate spheroidal, 265
parabolic, 263
parabolic cylindrical, 265
paraboloidal, 265
polar, 267
prolate spheroidal, 264
semiparabolic, 266
spherical, 261
CoordTrafo, 259, 269
Cornu spiral, 31
Cos-integral, 13
Coulomb phase shift, 103
Coulombscatt, 103
Coulomb scattering amplitude, 111
Coulombwave, 103
Coulomb wave function, 101, 105
F l , 103
f l , 104
G l , 104
H
±
l , 103
h l , 104
parabolic coordinates, 102
partial wave, 102
spherical coordinates, 102, 103
Cs, 132
C2hyper, 259, 275
Cylinder functions, 71
D
DawsonC, 23, 28
Dawson integral, 23, 27
Dc, 132
DedeEta, 123, 128
Dedekind η function, 123, 128
Dedekind sum, 127
DHexample.m, 243
Digamma function, 2, 7
DiincgammaC, 2, 11
Discriminant, 153
Dn, 132
Ds, 132
E
Edal2c, 272
Eiga, 166, 177
Eigb, 166, 177
EllipFun, 132, 135
EllipInt, 139, 149
EllipIntQuadtest.m, 150
Ellipj, 132
Ellipke, 139
Elliptic functions, 131
Elliptic integral
Bulirsch, 140
Carlson, 140
cel, 140, 149
D, 139, 142
E, 139, 141
el1, 140, 148
el2, 140, 148
el3, 140, 148
F, 139, 140
first kind, 131, 139
K, 139, 140
Π , 139, 141
RC, 140, 142
RD, 140
RF, 140, 143
RG, 140, 144
RJ, 140
second kind, 139
third kind, 139, 141
Elliptic modular function, 153, 155
ElliptIntQuadTest, 140