Index Z

zero potential
- Coulomb functions §33.22(ii), §33.22(ii), §33.22(ii)
zeros
- of orthogonal polynomials §18.2(vi)
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(i), §10.21(ix)—§10.21(ix)
- computation §10.74(vi), §10.74(vi)—§10.74(vi)
- distribution §10.21(i), §10.21(ix)—§10.21(xiii)
- 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 ( $\nu$ -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.
Zhedanov algebra §18.38(iii)
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)