x
Preface
Table 3 Special functions J–M
Function name
Notation
Section
Jacobi elliptic function
sn(z, k), ns(z, k)
10.2
Jacobi elliptic function
cn(z, k), nc(z, k)
10.2
Jacobi elliptic function
dn(z, k), nd(z, k)
10.2
Jacobi elliptic function
sd(z, k), ds(z, k)
10.2
Jacobi elliptic function
cd(z, k), dc(z, k)
10.2
Jacobi elliptic function
sc(z, k), cs(z, k)
10.2
Jacobi polynomial
P
(α,β)
n
(x)
15.5
Jacobi elliptic function
am(z, k)
10.2
Jacobi symbol
a
b
9.4
Jacobi ϑ functions
ϑ n (z, τ ), n ∈ {1, 2, 3, 4}
9.2
Jacobi zeta function
Z(β, k)
11.2
Kelvin functions
bei ν (z), ber ν (z)
4.3.4
Kelvin functions
kei ν (z), ker ν (z)
4.3.4
Klein’s complete invariant
J (τ )
12.2
Krawtchonk polynomials
K n (x; p, N)
8.3
Lagrange interpolation polynomial
Φ(x)
21.1
Laguerre polynomial
L α
n (x)
17.1
Lattice invariants
g2(Ω 1 , Ω 3 ), g3(Ω 1 , Ω 3 )
12.2
Lattice roots
e i (Ω 1 , Ω 3 ), i ∈ {1, 2, 3}
12.2
Legendre function, second kind
Q n (x)
3.2
Legendre function, second kind
Q
m
l (x)
3.3
Legendre function, second kind
Q
μ
ν (x)
3.4
Legendre function, associate
P m
l (x)
3.3
Legendre function, associate
P
μ
ν (z)
3.4
Legendre elliptic integral of first kind
K(k), F (φ, k)
11.2
Legendre elliptic integral of second kind
E(k), E(φ, k)
11.2
Legendre elliptic integral of third kind
Π(n, k), Π(φ, n, k)
11.2
Legendre polynomial
P n (x)
3.2
Mathieu function
ce ν (q, z), se ν (q, z)
14.2
Mathieu function
me ν (q, z)
14.2
Mathieu function, second solution
f e n (q, z), ge n (q, z)
14.2
Modified Mathieu function
Ce ν (q, z), Se ν (q, z)
14.2
Modified Mathieu function
Me ν (q, z)
14.2
Modified Mathieu function, second solution
F e n (q, z), Ge n (q, z)
14.2
Mehler function, first kind
P
μ
− 1
2 +iτ
(z)
3.4
Mehler function, second kind
Q
μ
−
1
2 +iτ
(z)
3.4
Meixner polynomial
M n (x; β, c)
8.3
Meixner–Pollaczek polynomial
P λ
n (x; Φ)
8.3