Index E
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ecological systems
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Einstein functions §4.44
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Einstein summation convention for vectors ¶ ‣ §1.6(ii), ¶ ‣ §1.6(ii)
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Eisenstein convention §23.8(ii)
-
Eisenstein series
-
electric particle field
-
electromagnetic scattering
-
Bessel functions and spherical Bessel functions §10.73(i)
-
electromagnetic theory
-
sine and cosine integrals §6.17
-
electromagnetic waves
-
electronic structure of heavy elements
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electron-ion collisions
-
electrostatics
-
elementary functions, see exponential function, hyperbolic functions, inverse hyperbolic functions, inverse trigonometric functions, Lambert
-function, logarithm function, power function, and trigonometric functions.
-
elementary particle physics
-
ellipse
-
ellipse arc length
-
ellipsoid
-
ellipsoidal coordinates §29.18(ii)
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ellipsoidal harmonics
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ellipsoidal wave equation, see Lamé wave equation.
-
elliptical coordinates
-
elliptic coordinates §31.17(i)
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elliptic crack and punch problems
-
elliptic curves §22.18(iv)
-
elliptic functions, see also Jacobian elliptic functions, and Weierstrass elliptic functions.
-
elliptic integrals, see basic elliptic integrals, Bulirsch’s elliptic integrals, general elliptic integrals, generalizations of elliptic integrals, Legendre’s elliptic integrals, and symmetric elliptic integrals.
-
complete
-
relations to other functions
-
elliptic modular function, see modular functions.
-
elliptic umbilic bifurcation set
-
elliptic umbilic canonical integral ¶ ‣ §36.2(i)
-
asymptotic approximations §36.11, §36.12(iii)
-
convergent series §36.8
-
differential equations §36.10(iii)
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formulas for Stokes set §36.5(iii)
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integral identity (36.9.9)
-
picture of Stokes set Figure 36.5.8, Figure 36.5.8
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pictures of modulus Figure 36.3.6, Figure 36.3.6, Figure 36.3.7, Figure 36.3.7, Figure 36.3.8, Figure 36.3.8
-
pictures of phase Figure 36.3.15, Figure 36.3.15, Figure 36.3.16, Figure 36.3.16, Figure 36.3.17, Figure 36.3.17
-
scaling laws §36.6
-
zeros §36.7(iii)
-
elliptic umbilic catastrophe ¶ ‣ §36.2(i), Figure 36.5.5, Figure 36.5.5
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entire functions ¶ ‣ §1.9(ii)
-
enumerative topology
-
epsilon function, see Jacobi’s epsilon function.
-
equation of Ince, see Hill’s equation, equation of Ince.
-
equiconvergent §30.4(iv)
-
Erlang loss function
-
incomplete gamma functions §8.23
-
error-control function
-
error functions §7.2(i)
-
applications
-
approximations §7.24(i), §7.24(ii), §7.24(ii), §7.24(i), §7.24(ii)
-
asymptotic expansions §7.12(i)
-
computation ¶ ‣ §3.5(ix), §7.22(i)
-
continued fractions §7.9
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definitions §7.2(i)
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derivatives §7.10
-
expansions in spherical Bessel functions §7.6(ii)
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generalized §7.16
-
graphics Figure 7.3.1, Figure 7.3.1, Figure 7.3.5, Figure 7.3.5, Figure 7.3.6, Figure 7.3.6
-
inequalities §7.8
-
integral representations §7.7(i), §7.7(i)
-
integrals
-
interrelations §7.5
-
inverse functions §7.17(i)
-
notation §7.1
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power-series expansions §7.6(i)
-
relations to other functions
-
repeated integrals of, see repeated integrals of the complementary error function.
-
sums §7.15
-
tables §7.23(ii), §7.23(iii), §7.23(ii), §7.23(iii)
-
values at infinity ¶ ‣ §7.2(i)
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zeros §7.13(i), §7.13(ii)
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error measures
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error term §2.3(i)
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essential singularity §1.10(iii), see also isolated essential singularity.
-
eta function, see Dedekind’s eta function.
-
Euler–Fermat theorem
-
Eulerian numbers
-
Euler–Maclaurin formula §2.10(i)
-
Euler numbers ¶ ‣ §24.1
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Euler–Poisson–Darboux equation
-
Euler–Poisson differential equations §19.18(ii)
-
Euler polynomials ¶ ‣ §24.1
-
Euler product
-
Euler’s beta integral ¶ ‣ §5.12
-
Euler’s constant §5.2(ii)
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Euler’s homogeneity relation
-
Euler’s integral
-
Euler’s pentagonal number theorem
-
Euler splines ¶ ‣ §24.17(ii)
-
Euler’s totient
-
Euler’s transformation
-
Euler sums
-
Euler–Tricomi equation
-
evolution equations
-
exact rational arithmetic §3.1(iii)
-
exponential function §4.2(iii)
-
exponential growth ¶ ‣ §1.14(iii)
-
exponential integrals §6.2(i)
-
analytic continuation §6.4
-
applications §6.17
-
approximations §6.20(i), §6.20(i), §6.20(i)
-
asymptotic expansions §6.12(i)
-
Chebyshev-series expansions §6.20(ii), §6.20(ii), §6.20(ii), §6.20(ii), §6.20(ii)
-
computation §6.18
-
continued fraction §6.9
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definition §6.2(i)
-
expansion in inverse factorials §6.10(i)
-
expansions in modified spherical Bessel functions §6.10(ii)
-
generalized §8.19
-
graphics Figure 6.3.1, Figure 6.3.1, Figure 6.3.3, Figure 6.3.3
-
inequalities §6.8
-
integral representations §6.7, §6.7(i)
-
integrals §6.14(i), §6.14(ii)
-
interrelations §6.2(i), §6.5
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Laplace transform §6.14(i)
-
notation §6.1
-
power series §6.6
-
principal value §6.2(i)
-
relations to other functions
-
small argument ¶ ‣ §2.5(iii)
-
tables §6.19(ii), §6.19(ii), §6.19(iii), §6.19(iii)
-
zeros §6.13
-
extended complex plane §1.9(iv)