DLMF: Index Z
Keywords: Coulomb functions, Descartes’ rule of signs, Horner’s scheme, Laplace integral, analytic properties, applications, approximations, asymptotic expansions, asymptotic expansions for large order, asymptotic expansions for large zeros, beta integral, bounds, common, complex, computation, conditioning, definition, degrees two, three, four, discriminant, distribution, division algorithm, double, elementary properties, elementary symmetric functions, error bounds, explicit formulas, extended, forward differences, interlacing, mean-value, monotonicity, multiplicity, normalization, notation, of cross-products, orthogonality, purely imaginary, relation to inverse phase functions, resolvent cubic, roots of constants, roots of unity, simple, summation, tables, ultraspherical polynomials, uniform, with respect to order (, zero potential, zeros of Bessel functions (including derivatives), zeros of analytic functions, zeros of cylinder functions (including derivatives), zeros of polynomials, zeta fun [cell cut: 1051 characters, first 1000 kept]

Index Index W Notations

# Index Z

- zero potential
  - Coulomb functions ¶ ‣ §33.22(ii), ¶ ‣ §33.22(ii), ¶ ‣ §33.22(ii)
- zeros of analytic functions
  - computation §3.8, ¶ ‣ §3.8(vi)
  - conditioning §3.8(vi)
  - multiplicity ¶ ‣ §1.10(i), §3.8
  - simple §3.8
- zeros of Bessel functions (including derivatives)
  - analytic properties §10.21(ii), §10.21(ii)
  - approximations ¶ ‣ §10.76(ii)
  - asymptotic expansions for large order
    - uniform §10.21(viii)
  - asymptotic expansions for large zeros §10.21(vi)
    - error bounds §10.21(vi)
  - bounds §10.21(v)
  - common §10.21(i)
  - complex ¶ ‣ §10.21(ix), §10.21(i), §10.21(ix)
  - computation ¶ ‣ §10.74(vi), §10.74(vi)
  - distribution §10.21(i), §10.21(xiii), §10.21(ix)
  - double §10.21(i)
  - interlacing §10.21(i)
  - monotonicity §10.21(iv)
  - notation §10.21(i)
  - of cross-products §10.21(x)
    - asymptotic expansions §10.21(x)
  - purely imaginary §10.21(i), §10.21(v)
  - relation to inverse phase functions §10.21(ii)
  - tables §10.75(iii), §4.46
  - with respect to order (ν-zeros) §10.21(xiv)
- zeros of cylinder functions (including derivatives) §10.21(i), §10.21(vii)
  - analytic properties §10.21(ii)
  - asymptotic expansions for large order
    - uniform §10.21(vii)
  - asymptotic expansions for large zeros §10.21(vi)
  - forward differences §10.21(ii)
  - interlacing §10.21(i)
  - monotonicity §10.21(iv)
  - relation to inverse phase functions §10.21(ii)

- zeros of polynomials, see also stable polynomials.
  - computation ¶ ‣ §3.8(iv), §3.8(iv)
  - conditioning §3.8(vi)
  - degrees two, three, four §1.11(iii)
  - Descartes’ rule of signs ¶ ‣ §1.11(ii)
  - discriminant ¶ ‣ §1.11(ii)
  - distribution ¶ ‣ §1.11(ii), §1.11(ii)
  - division algorithm §1.11(i)
  - elementary properties §1.11(ii)
  - elementary symmetric functions ¶ ‣ §1.11(ii)
  - explicit formulas §3.8(iv)
  - Horner’s scheme ¶ ‣ §1.11(i)
    - extended ¶ ‣ §1.11(i)
  - resolvent cubic ¶ ‣ §1.11(iii)
  - roots of constants §1.11(iv)
  - roots of unity §1.11(iv)
- zeta function, see Hurwitz zeta function, Jacobi’s zeta function, periodic zeta function, Riemann zeta function, and Weierstrass zeta function.
- zonal polynomials §35.4
  - applications §35.9
  - beta integral ¶ ‣ §35.4(ii)
  - definition §35.4(i)
  - Laplace integral ¶ ‣ §35.4(ii)
  - mean-value ¶ ‣ §35.4(ii)
  - normalization ¶ ‣ §35.4(ii)
  - notation §35.4(i)
  - orthogonality ¶ ‣ §35.4(ii)
  - summation ¶ ‣ §35.4(ii)
  - tables §35.11
- zonal spherical harmonics
  - ultraspherical polynomials ¶ ‣ §18.38(ii)