Preface
ix
Table 2 Special functions D–H
Function name
Notation
Section
Dawson integral
F (z)
2.2
Dedekind’s η function
η(τ )
9.3
Digamma function
ψ(z)
1.4
Discriminant
Δ(Ω 1 , Ω 3 )
12.2
Elliptic integral of first kind
K(k), F (φ, k)
11.2
Elliptic integral of second kind
E(k), E(φ, k)
11.2
Elliptic integral of third kind
Π(n, k), Π(φ, n, k)
11.2
Elliptic integral, symmetric
D(φ, k)
11.2
Elliptic modular function
λ(τ )
12.2
Error function
erf (z)
2.2
Error function, complementary
erf c(z)
2.2
Euler polynomial
E n (x)
19.2
Euler number
E n
19.2
Fresnel integral
F F (z)
2.4
Fresnel integral, cosine
C(z)
2.4
Fresnel integral, sine
S(z)
2.4
Gamma function
Γ (z)
1.2
Gamma function, incomplete
Γ (z, a)
1.5
Gamma function, inverse incomplete
1.5
Gauss hypergeometric function
2 F 1 (a, b; c; z)
8
Gegenbauer polynomial
C λ
n (x)
15.4
Hankel function
H
(n)
ν (z), n ∈ {1, 2}
4.3
Harmonic oscillator states
ψ n (x)
16.3
Hermite interpolation polynomial
Φ(x), ¯
Φ(x)
21.1
Hermite interpolation polynomial, extended
Φ(x), ¯
Φ(x) ¯ ¯
Φ(x)
21.1
Hermite polynomials
H n (x)
16.2
Heumann’s lambda function
Λ 0 (β, k)
11.2
Hypergeometric function
2 F 0 (a, b, z)
6.1
Hypergeometric function
2 F 1 (a, b; c; z)
8