Digital Library of Mathematical Functions
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Notations

Notations E

*ABCD♦E♦FGHIJKLMNOPQRSTUVWXYZ
element of; Common Notations and Definitions
not an element of; Common Notations and Definitions
base of exponential function; (4.2.11)
En
Euler numbers; 24.2(ii)
En()
generalized Euler numbers; 24.16(i)
E(α)=E(k)
notation used by Abramowitz and Stegun (1964, Chapter 17); 19.1
(with E(k): Legendre’s complete elliptic integral of the second kind)
E(k)
Legendre’s complete elliptic integral of the second kind; (19.2.8)
η(τ)
Dedekind’s eta function (or Dedekind modular function); (23.15.9)
η(τ)
Dedekind’s eta function (or Dedekind modular function); (27.14.12)
Es(z)
elementary symmetric function; (19.19.4)
En(x)
Euler polynomials; 24.2(ii)
E1(z)
exponential integral; (6.2.1)
Ep(z)
generalized exponential integral; (8.19.1)
Ea,b(z)
Mittag-Leffler function; (10.46.3)
Eq(x)
q-exponential function; (17.3.2)
Eν(z)
Weber function; (11.10.2)
eq(x)
q-exponential function; (17.3.1)
e0(x)=πHi(-x)
notation used by Tumarkin (1959); 9.1
(with Hi(z): Scorer function (inhomogeneous Airy function))
e~0(x)=-πGi(-x)
notation used by (Tumarkin, 1959); 9.1
(with Gi(z): Scorer function (inhomogeneous Airy function))
E~n(x)
periodic Euler functions; 24.2(iii)
E(k)
Legendre’s complementary complete elliptic integral of the second kind; (19.2.9)
En()(x)
generalized Euler polynomials; 24.16(i)
E(ϕ\α)=E(ϕ,k)
notation used by Abramowitz and Stegun (1964, Chapter 17); 19.1
(with E(ϕ,k): Legendre’s incomplete elliptic integral of the second kind)
E(ϕ,k)
Legendre’s incomplete elliptic integral of the second kind; (19.2.5)
Ecν2m(z,k2)Ecν2m(z,k2)
notation used by Ince (1940b); 29.1
(with Ecνm(z,k2): Lamé function)
Ecν2m+1(z,k2)Esν2m+1(z,k2)
notation used by Ince (1940b); 29.1
(with Esνm(z,k2): Lamé function)
Ecνm(z,k2)
Lamé function; 29.3(iv)
Ei(x)
exponential integral; 6.2(i)
Ein(z)
complementary exponential integral; (6.2.3)
el1(x,kc)
Bulirsch’s incomplete elliptic integral of the first kind; (19.2.15)
el2(x,kc,a,b)
Bulirsch’s incomplete elliptic integral of the second kind; (19.2.12)
el3(x,kc,p)
Bulirsch’s incomplete elliptic integral of the third kind; (19.2.16)
envAi(x)
envelope of Airy function; (2.8.20)
envBi(x)
envelope of Airy function; (2.8.20)
envJν(x)
envelope of Bessel function; (2.8.33)
envYν(x)
envelope of Bessel function; (2.8.33)
envU(-c,x)
envelope of parabolic cylinder function; 14.15(v)
envU¯(-c,x)
envelope of parabolic cylinder function; 14.15(v)
ϵj,k,
Levi-Civita symbol; (1.6.14)
(x,k)
Jacobi’s epsilon function; (22.16.14)
Erfz=12πerfz
alternative notation for the error function; 7.1
(with erfz: error function)
erfz
error function; (7.2.1)
erfcz
complementary error function; (7.2.2)
Erfiz=z2F(z)
alternative notation for Dawson’s integral; 7.1
(with F(z): Dawson’s integral and : base of exponential function)
Esν2m+1(z,k2)Ecν2m+1(z,k2)
notation used by Ince (1940b); 29.1
(with Ecνm(z,k2): Lamé function)
Esν2m+2(z,k2)Esν2m+2(z,k2)
notation used by Ince (1940b); 29.1
(with Esνm(z,k2): Lamé function)
Esνm(z,k2)
Lamé function; 29.3(iv)
etr(X)
exponential of trace; 35.1
expz
exponential function; (4.2.19)