280
Index
K
Kei, 77
Kelvin functions, 66, 77
bei, 77
ber, 77
kei, 77
ker, 77
Ker, 77
Klein’s complete invariant, 153
Klein’s complete invariant J, 155
Krawtchonk polynomials, 121
K2tau2k, 138
K2tK, 132, 138
Kummer equation, 92
Kummer functions, 92
Kummer transformation, 93, 94
L
Lagrange interpolation polynomial, 238
Lagrange interpolation polynomial, linear
equations, 238
Laguerrepoly, 211, 213
Laguerre polynomial, 201, 211
generalized, 212
generating function, 213
Jacobi matrix, 213
Rodrigues formula, 212
Laguerrex, 211, 213
plot, 214
Laguerrezero, 211, 214
Laplace-Beltrami operator, 260
cylindrical coordinates, 263
parabolic coordinates, 264
semiparabolic coordinate, 266
spherical coordinates, 261
Lattice discriminant, 155
Lattice invariants, 153, 155
Lattice roots, 153, 155
Legendre differential equation, 35
Legendrefun, 43
methods, 43
Legendre functions, 41
complex, 46
first kind, 34, 35
hypergeometric series, 46
second kind, 34, 35
Legendrepoly, 34, 36
deri, 37
plot, 37
polyvalue, 37
Legendre polynomial, 33, 35, 193
derivative, 37
Jacobi matrix, 41
nodes, 40
Rodrigues formula, 35
2nd kind, 39
Legendre-symbol, 129
Legendre2poly, 34, 39
Line broadening function, 24, 29
Local basis, 245, 247
Local matrices, 247
M
Mathieu equation, 165
modified, 165
Mathieudeq, 178
Mathieudgl, 166
MathieuFun, 166, 174
Mathieu function
ce, 166, 170–172
fe, 166, 170, 172
ge, 166, 170, 172
me, 166, 171, 172
noninteger, 171
se, 166, 170–172
second solution, 170
w I , 166, 170, 173
w II , 166, 170, 173
Mehlerfun, 34, 51
Mehler function, 34, 51
1st kind, 52
2nd kind, 54
Meixner-Pollaczek polynomials, 121
Meixner polynomials, 121
Modified Bessel functions, 74
Modmathieudeq, 178
N
Nc, 132
Nchoosek, 16
Nd, 132
Neumann functions, 71
Nome, 124
Normal distribution, 27
N-particle systems, 267
Ns, 132
O
Oblate spheroidal functions, 35, 62
Orthogonal polynomials, 182
approximation, 223
coordinate range, 218
Orthogonal polynomials, three-term recurrence
relation, 183
Index
K
Kei, 77
Kelvin functions, 66, 77
bei, 77
ber, 77
kei, 77
ker, 77
Ker, 77
Klein’s complete invariant, 153
Klein’s complete invariant J, 155
Krawtchonk polynomials, 121
K2tau2k, 138
K2tK, 132, 138
Kummer equation, 92
Kummer functions, 92
Kummer transformation, 93, 94
L
Lagrange interpolation polynomial, 238
Lagrange interpolation polynomial, linear
equations, 238
Laguerrepoly, 211, 213
Laguerre polynomial, 201, 211
generalized, 212
generating function, 213
Jacobi matrix, 213
Rodrigues formula, 212
Laguerrex, 211, 213
plot, 214
Laguerrezero, 211, 214
Laplace-Beltrami operator, 260
cylindrical coordinates, 263
parabolic coordinates, 264
semiparabolic coordinate, 266
spherical coordinates, 261
Lattice discriminant, 155
Lattice invariants, 153, 155
Lattice roots, 153, 155
Legendre differential equation, 35
Legendrefun, 43
methods, 43
Legendre functions, 41
complex, 46
first kind, 34, 35
hypergeometric series, 46
second kind, 34, 35
Legendrepoly, 34, 36
deri, 37
plot, 37
polyvalue, 37
Legendre polynomial, 33, 35, 193
derivative, 37
Jacobi matrix, 41
nodes, 40
Rodrigues formula, 35
2nd kind, 39
Legendre-symbol, 129
Legendre2poly, 34, 39
Line broadening function, 24, 29
Local basis, 245, 247
Local matrices, 247
M
Mathieu equation, 165
modified, 165
Mathieudeq, 178
Mathieudgl, 166
MathieuFun, 166, 174
Mathieu function
ce, 166, 170–172
fe, 166, 170, 172
ge, 166, 170, 172
me, 166, 171, 172
noninteger, 171
se, 166, 170–172
second solution, 170
w I , 166, 170, 173
w II , 166, 170, 173
Mehlerfun, 34, 51
Mehler function, 34, 51
1st kind, 52
2nd kind, 54
Meixner-Pollaczek polynomials, 121
Meixner polynomials, 121
Modified Bessel functions, 74
Modmathieudeq, 178
N
Nc, 132
Nchoosek, 16
Nd, 132
Neumann functions, 71
Nome, 124
Normal distribution, 27
N-particle systems, 267
Ns, 132
O
Oblate spheroidal functions, 35, 62
Orthogonal polynomials, 182
approximation, 223
coordinate range, 218
Orthogonal polynomials, three-term recurrence
relation, 183