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Notations

Notations E

*ABCD♦E♦FGHIJKLMNOPQRSTUVWXYZ
equals by definition; Common Notations and Definitions
e
base of natural logarithm; (4.2.11)
element of; Common Notations and Definitions
not an element of; Common Notations and Definitions
E n
Euler numbers; §24.2(ii)
E n ( )
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); (27.14.12)
E 1 ( z )
exponential integral; (6.2.1)
E ( k )
Legendre’s complementary complete elliptic integral of the second kind; (19.2.9)
e 0 ( x ) = π Hi ( - x )
notation used by Tumarkin (1959); §9.1
(with Hi(z): Scorer function (inhomogeneous Airy function) and π: the ratio of the circumference of a circle to its diameter)
e ~ 0 ( x ) = - π Gi ( - x )
notation used by (Tumarkin, 1959); §9.1
(with Gi(z): Scorer function (inhomogeneous Airy function) and π: the ratio of the circumference of a circle to its diameter)
E a , b ( z )
Mittag-Leffler function; (10.46.3)
E n ( x )
Euler polynomials; §24.2(ii)
E ν ( z )
Weber function; (11.10.2)
E p ( z )
generalized exponential integral; (8.19.1)
E q ( x )
q-exponential function; (17.3.2)
e q ( x )
q-exponential function; (17.3.1)
E s ( z )
elementary symmetric function; (19.19.4)
E n ( ) ( x )
generalized Euler polynomials; §24.16(i)
E ~ n ( x )
periodic Euler functions; §24.2(iii)
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)
e j
Weierstrass lattice roots; §23.3(i)
Ec ν 2 m ( z , k 2 ) Ec ν 2 m ( z , k 2 )
notation used by Ince (1940b); §29.1
(with Ecνm(z,k2): Lamé function)
Ec ν 2 m + 1 ( z , k 2 ) Es ν 2 m + 1 ( z , k 2 )
notation used by Ince (1940b); §29.1
(with Esνm(z,k2): Lamé function)
Ec ν m ( z , k 2 )
Lamé function; §29.3(iv)
Ei ( x )
exponential integral; §6.2(i)
Ein ( z )
complementary exponential integral; (6.2.3)
el1 ( x , k c )
Bulirsch’s incomplete elliptic integral of the first kind; (19.2.15)
el2 ( x , k c , a , b )
Bulirsch’s incomplete elliptic integral of the second kind; (19.2.12)
el3 ( x , k c , p )
Bulirsch’s incomplete elliptic integral of the third kind; (19.2.16)
envAi ( x )
envelope of Airy function Ai(x); §2.8(iii)
envBi ( x )
envelope of Airy function Bi(x); §2.8(iii)
env J ν ( x )
envelope of Bessel function Jν(x); §2.8(iv)
env Y ν ( x )
envelope of Bessel function Yν(x); §2.8(iv)
env U ( c , x )
envelope of parabolic cylinder function U(c,x); §14.15(v)
env U ¯ ( c , x )
envelope of parabolic cylinder function U¯(c,x); §14.15(v)
ϵ j k
Levi-Civita symbol; (1.6.14)
( x , k )
Jacobi’s epsilon function; (22.16.14)
modular equivalence; Common Notations and Definitions
Erf z = 1 2 π erf z
alternative notation for the error function; §7.1
(with π: the ratio of the circumference of a circle to its diameter and erfz: error function)
erf z
error function; (7.2.1)
erfc z
complementary error function; (7.2.2)
Erfi z = e z 2 F ( z )
alternative notation for Dawson’s integral; §7.1
(with F(z): Dawson’s integral and e: base of natural logarithm)
Es ν 2 m + 1 ( z , k 2 ) Ec ν 2 m + 1 ( z , k 2 )
notation used by Ince (1940b); §29.1
(with Ecνm(z,k2): Lamé function)
Es ν 2 m + 2 ( z , k 2 ) Es ν 2 m + 2 ( z , k 2 )
notation used by Ince (1940b); §29.1
(with Esνm(z,k2): Lamé function)
Es ν m ( z , k 2 )
Lamé function; §29.3(iv)
etr ( X )
exponential of trace; §35.1
exp z
exponential function; (4.2.19)