Index S
-
spline functions
-
splines
-
square-integrable function
§1.4(v)
-
stability problems
-
stable polynomials
§1.11(v)
-
statistical analysis
-
multivariate
-
functions of matrix argument
§35.9
-
statistical applications
-
functions of matrix argument
§35.9
-
statistical mechanics
-
statistical physics
-
Bernoulli and Euler polynomials
§24.18
-
Painlevé transcendents
§32.16
-
Steed’s algorithm
-
steepest-descent paths
-
Stickelberger codes
-
Stieltjes fraction (-fraction)
§3.10(ii)
-
Stieltjes polynomials
-
Stieltjes transform
-
Stieltjes–Wigert polynomials
§18.27(vi)
-
asymptotic approximations
§18.29
-
Stirling cycle numbers
§26.13
-
Stirling numbers (first and second kinds)
-
Stirling’s formula
§5.11(i)
-
Stirling’s series
§5.11(i)
-
Stokes line
§2.11(iv)
-
Stokes multipliers
§2.7(ii)
-
Stokes phenomenon
§2.11(iv)
-
Stokes sets
§36.5(i)—§36.5(iv)
-
Stokes’ theorem for vector-valued functions
§1.6(v)
-
string theory
-
Struve functions, see Struve functions and modified Struve functions.
-
Struve functions and modified Struve functions
Ch.11
-
analytic continuation
§11.4(iii)
-
applications
-
approximations
§11.15(i)
-
argument
§11.8
-
asymptotic expansions
-
computation
§11.13(i)
-
definitions
§11.2
-
derivatives
§11.4(v)
-
differential equations
§11.2(ii)—§11.2(iii)
-
graphics Figure 11.3.1, Figure 11.3.1, Figure 11.3.1, Figure 11.3.10, Figure 11.3.10, Figure 11.3.10, Figure 11.3.11, Figure 11.3.11, Figure 11.3.11, Figure 11.3.12, Figure 11.3.12, Figure 11.3.12, Figure 11.3.13, Figure 11.3.13, Figure 11.3.13, Figure 11.3.14, Figure 11.3.14, Figure 11.3.14, Figure 11.3.15, Figure 11.3.15, Figure 11.3.15, Figure 11.3.16, Figure 11.3.16, Figure 11.3.16, Figure 11.3.17, Figure 11.3.17, Figure 11.3.17, Figure 11.3.18, Figure 11.3.18, Figure 11.3.18, Figure 11.3.19, Figure 11.3.19, Figure 11.3.19, Figure 11.3.2, Figure 11.3.2, Figure 11.3.2, Figure 11.3.20, Figure 11.3.20, Figure 11.3.20, Figure 11.3.3, Figure 11.3.3, Figure 11.3.3, Figure 11.3.4, Figure 11.3.4, Figure 11.3.4, Figure 11.3.5, Figure 11.3.5, Figure 11.3.5, Figure 11.3.6, Figure 11.3.6, Figure 11.3.6, Figure 11.3.7, Figure 11.3.7, Figure 11.3.7, Figure 11.3.8, Figure 11.3.8, Figure 11.3.8, Figure 11.3.9, Figure 11.3.9, Figure 11.3.9
-
half-integer orders
§11.4(i)
-
incomplete
§11.14(v)
-
inequalities
§11.4(ii)
-
integral representations
-
integrals
-
Kelvin-function analogs
§11.8
-
notation
§11.1
-
order
§11.1
-
power series
§11.2(i)
-
principal values
§11.2(i)
-
recurrence relations
§11.4(v)
-
relations to Anger–Weber functions
§11.10(vi)
-
series expansions
-
sums
§11.7(v)
-
tables
§11.14(ii)
-
zeros
§11.4(vii)
-
Struve’s equation, see Struve functions and modified Struve functions, differential equations.
-
Sturm–Liouville eigenvalue problems
-
ordinary differential equations
§3.7(iv)
-
summability methods for integrals
-
summability methods for series
-
summation by parts
§2.10(ii)
-
summation formulas
-
sums of powers
-
supersonic flow
-
support
-
surface, see parametrized surfaces.
-
surface harmonics of the first kind
§14.30(i)
-
surface-wave problems
-
swallowtail bifurcation set
-
swallowtail canonical integral
§36.2(i)
-
asymptotic approximations
§36.11—§36.12(iii)
-
convergent series
§36.8
-
differential equations
§36.10(ii)
-
formulas for Stokes set
§36.5(ii)
-
integral identities
§36.9
-
picture of Stokes set
§36.5(iv)
-
pictures of modulus Figure 36.3.2, Figure 36.3.2, Figure 36.3.2, Figure 36.3.3, Figure 36.3.3, Figure 36.3.3, Figure 36.3.4, Figure 36.3.4, Figure 36.3.4, Figure 36.3.5, Figure 36.3.5, Figure 36.3.5
-
pictures of phase Figure 36.3.14, Figure 36.3.14
-
scaling laws
§36.6
-
zeros
§36.7(iv)
-
swallowtail catastrophe §36.2(i), Figure 36.5.2, Figure 36.5.2, Figure 36.5.3, Figure 36.5.3, Figure 36.5.4, Figure 36.5.4, Figure 36.5.7, Figure 36.5.7
-
symmetric elliptic integrals
§19.16(i)
-
addition theorems
§19.26—§19.26(iii)
-
advantages of symmetry
§19.15—§19.15
-
applications
-
arithmetic-geometric mean
§19.22(ii)
-
asymptotic approximations and expansions §19.27—§19.27(vi), §2.6(ii)
-
Bartky’s transformation
§19.22(i)
-
change of parameter of
§19.21(iii)
-
circular cases §19.20(iii)—§19.20(iii), §19.21(iii)
-
complete
§19.1
-
computation
§19.36—§19.38
-
connection formulas
§19.21
-
degree
§19.16(ii)
-
derivatives
§19.18(i)
-
differential equations §19.18(ii), §19.18(ii)
-
duplication formulas
§19.26(iii)
-
elliptic cases of
§19.16(iii)
-
first, second, and third kinds
§19.1
-
Gauss transformations §19.15, §19.22(iii)—§19.22(iii)
-
general lemniscatic case §19.20(i), §19.20(iv)
-
graphics
§19.17—§19.17
-
hyperbolic cases §19.20(iii)—§19.20(iii), §19.21(iii)
-
inequalities
-
integral representations
§19.23
-
integrals of
§19.28—§19.28
-
Landen transformations §19.15, §19.22(iii)—§19.22(iii)
-
notation
§19.1
-
permutation symmetry §19.15, §19.16(ii)
-
power-series expansions
§19.19—§19.19
-
reduction of general elliptic integrals
§19.29—§19.29(iii)
-
relations to other functions
-
special cases
§19.20—§19.20(v)
-
tables
§19.37(iv)
-
transformations replaced by symmetry §19.15, §19.22(iii), §19.25(i)
-
symmetries
-
Szegő–Askey polynomials
§18.33(iv)
-
Szegő–Szász inequality