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Notations E

*ABCD♦E♦FGHIJKLMNOPQRSTUVWXYZ
element of; Common Notations and Definitions
not an element of; Common Notations and Definitions
e
base of exponential function; 4.2.11
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 s ( z )
elementary symmetric function; 19.19.4
E n ( x )
Euler polynomials; §24.2(ii)
E 1 ( z )
exponential integral; 6.2.1
E p ( z )
generalized exponential integral; 8.19.1
E a , b ( z )
Mittag-Leffler function; 10.46.3
E q ( x )
q-exponential function; 17.3.2
E ν ( z )
Weber function; 11.10.2
e q ( x )
q-exponential function; 17.3.1
e 0 ( x ) = π Hi ( - x )
notation used by Tumarkin (1959); §9.1
(with Hi(z): Scorer function (inhomogeneous Airy function))
e ~ 0 ( x ) = - π Gi ( - 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
E n ( ) ( 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
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; 2.8.20
envBi ( x )
envelope of Airy function; 2.8.20
env J ν ( x )
envelope of Bessel function; 2.8.33
env Y ν ( x )
envelope of Bessel function; 2.8.33
env U ( - c , x )
envelope of parabolic cylinder function; §14.15(v)
env U ¯ ( - c , x )
envelope of parabolic cylinder function; §14.15(v)
ϵ j , k ,
Levi-Civita symbol; 1.6.14
( x , k )
Jacobi’s epsilon function; 22.16.14
Erf z = 1 2 π erf z
alternative notation for the error function; §7.1
(with 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 exponential function)
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