viii
Preface
Table 1 Special functions A–C
Function name
Notation
Section
Airy function
Ai(z)
4.2
Airy function
Bi(z)
4.2
Anger function
J ν (z)
5.3
Bernoulli polynomials
B n (x)
19.1
Bernoulli numbers
B n
19.1
Beta function
B(z, w)
1.7
Beta function, incomplete
B x (z, w)
1.7
Bessel function, first kind
J ν (z)
4.3
Bessel function, modified first kind
I ν (z)
4.3
Bessel function, modified second kind
K ν (z)
4.3
Bessel function, second kind
Y ν (z)
4.3
Bessel function, spherical first kind
j n (z)
4.3.3
Bessel function, spherical second kind
y n (z)
4.3.3
Bessel function, spherical third kind
h
(n)
n (z), n ∈ {1, 2}
4.3.3
Bessel function, spherical
i
(n)
n (z), n ∈ {1, 2}
4.3.3
Bessel function, spherical
k n (z)
4.3.3
Bessel function, third kind
H
(n)
ν (z), n ∈ {1, 2}
4.3
Burlirsch’s elliptic integrals
el1(x, kc), el2(x, kc, a, b)
11.2
Burlirsch’s elliptic integrals
el3(x, kc, a, b), cel(kc, p, a, b)
11.2
Carlson’s elliptic function
RC(x, y)
11.2
Carlson’s elliptic integral of first kind
RF (x, y, z)
11.2
Carlson’s elliptic integral of second kind
RG(x, y, z), RD(x, y, z)
11.2
Carlson’s elliptic integral of third kind
RJ (x, y, z, p)
11.2
Charlier polynomial
C n (x; a)
6.4
Chebyshev polynomial first kind, shifted
T n (x), T ∗
n (x)
18.1
Chebyshev polynomial second kind, shifted
U n (x), U ∗
n (x)
18.1
Chebyshev polynomial third kind, shifted
V n (x), V ∗
n (x)
18.1
Chebyshev polynomial fourth kind, shifted
W n (x), W ∗
n (x)
18.1
Clebsch-Gordan coefficient
C(·j ·; ·m·)
22.1.2
Coherent states
|α
16.3
Confluent hypergeometric function, first kind
1 F 1 (a, b, z)
6.1
Confluent hypergeometric function, second kind
U(a, b, z)
6.1
Confluent hypergeometric limit function
0 F 1 (a, b, z)
6.2
Conical function, first kind
P
μ
−
1
2 +iτ
(z)
3.4
Conical function, second kind
Q
μ
−
1
2 +iτ
(z)
3.4
Coulomb wave function, irregular
H
±
l (γ , ρ)
7.2.1
Coulomb wave function, irregular
h l ((, ζ )
7.2.1
Coulomb wave function, irregular
G
±
l (γ , ρ)
7.2.1
Coulomb wave function, regular
F
±
l (γ , ρ)
7.2.1
Coulomb wave function, regular
f
±
l ((, ζ )
7.2.1
Coulomb wave function, parabolic
ψ k (r)
7.2.2
Cylinder function
J ν (z)
4.3