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