Index M
-
-test for uniform convergence
-
magic squares
-
magnetic monopoles
-
Riemann theta functions
§21.9
-
Mangoldt’s function
-
many-body systems
-
many-valued function, see multivalued function.
-
Markov’s theorem
§18.2(x)
-
mathematical background
-
boundary conditions and the Weyl alternative
§1.18(ix)
-
essentially self-adjoint operator
§1.18(ix)
-
limit point and limit circle boundary conditions
§1.18(ix)
-
self-adjoint extensions of a symmetric operator
§1.18(ix)
-
self-adjoint operator
§1.18(ix)
-
spectrum of an operator
§1.18(ix)
-
mathematical constants
§3.12
-
Mathieu functions Ch.28, Ch.28, see also Mathieu’s equation, modified Mathieu functions, and radial Mathieu functions.
-
analytic properties §28.12(iii), §28.2(ii), §28.7
-
antiperiodicity
§28.2(vi)
-
applications
-
asymptotic expansions for large , see also uniform asymptotic approximations for large parameters.
-
computation
Ch.28—§28.34(iv)
-
connection formulas
§28.12(iii)
-
definitions
§28.12
-
differential equation
§28.2(i)
-
expansions in series of §28.11—§28.11, §28.19
-
Fourier coefficients
-
Fourier series §28.14, §28.2(iv), §28.4
-
graphics §28.13, §28.3—§28.3(ii)
-
integral equations
-
integral representations
§28.28(i)
-
integrals
-
irreducibility
§28.7
-
limiting forms as order tends to integers §28.12(ii), §28.12(iii)
-
normalization §28.12(ii), §28.2(vi)
-
notation
§28.1
-
of integer order
§28.2(vi)
-
of noninteger order
§28.12(ii)
-
orthogonality §28.12(ii), §28.2(vi)
-
parity
§28.2(vi)
-
periodicity §28.12(ii), §28.2(vi)
-
power series in §28.15(ii), §28.6(ii)
-
pseudoperiodicity §28.12(ii), §28.2(iv)
-
reflection properties in §28.12(ii), §28.12(iii), §28.2(vi)
-
reflection properties in
§28.12(ii)
-
reflection properties in
§28.12(ii)
-
relations to other functions
-
tables
§28.35—§28.35(ii)
-
uniform asymptotic approximations for large parameters
-
values at
§28.2(vi)
-
Wronskians
§28.5(i)
-
zeros
§28.9
-
Mathieu’s equation
§28.2(i)
-
matrix, see also linear algebra.
-
matrix elements of the resolvent
-
matrix exponential
-
matrix, index notation for m by n
§1.2(v)
-
maximum
§1.4(vii)
-
maximum-modulus principle
-
McKean and Moll’s theta functions
§20.1
-
McMahon’s asymptotic expansions
-
mean value property for harmonic functions
§1.9(iii)
-
mean value theorems
-
means, see Abel means, arithmetic mean, Cesàro means, geometric mean, harmonic mean, and weighted means.
-
measure
§18.2(i)
-
Mehler functions, see conical functions.
-
Mehler–Dirichlet formula
-
Mehler–Fock transformation §14.20(vi), §14.31(ii)
-
Mehler–Sonine integrals
-
Meijer -function
§16.17
-
Meixner polynomials, see Hahn class orthogonal polynomials.
-
relation to hypergeometric function
§15.9(i)
-
Meixner–Pollaczek polynomials, see Hahn class orthogonal polynomials.
-
Mellin transform
-
Mellin–Barnes integrals
§5.19(ii)
-
meromorphic function
§1.10(iii)
-
Mersenne numbers
-
Mersenne prime
-
method of stationary phase
-
asymptotic approximations of integrals
§2.3(iv)
-
metric coefficients
-
Mill’s ratio for complementary error function
§7.8
-
Miller’s algorithm
-
minimax polynomial approximations
§3.11(i)
-
minimax rational approximations
§3.11(iii)
-
minimum
§1.4(vii)
-
Minkowski’s inequalities for sums and series §1.7(i), §1.7(ii)
-
minor, see determinants.
-
Mittag-Leffler function
§10.46
-
Mittag-Leffler’s expansion
-
mixed spectra
-
Möbius function
-
Möbius inversion formulas
-
Möbius transformation, see bilinear transformation.
-
modified Bessel functions
Ch.10
-
addition theorems
§10.44(ii)
-
analytic continuation
§10.34
-
applications
-
approximations
§10.76(ii)
-
asymptotic expansions for large argument
§10.40—§10.40(iv)
-
asymptotic expansions for large order
§10.41—§10.41(v)
-
branch conventions
§10.25(ii)
-
computation
Ch.10—§10.74(v)
-
connection formulas
§10.27
-
continued fractions
§10.33
-
cross-products
§10.28
-
definitions
§10.25(i)
-
derivatives
-
derivatives with respect to order
§10.38
-
asymptotic expansion for large argument
§10.40(i)
-
differential equations §10.25(i), §10.36, see also modified Bessel’s equation.
-
generating function
§10.35
-
graphics
§10.26(i)
-
hyperasymptotic expansions
§10.74(i)
-
incomplete
§10.46
-
inequalities
§10.37
-
integral representations
-
integrals, see integrals of modified Bessel functions.
-
limiting forms
§10.30(i)
-
monotonicity
§10.37
-
multiplication theorem
§10.44(i)
-
notation
§10.1
-
of imaginary order
-
approximations
§10.76(ii)
-
computation
§10.74(viii)
-
definitions
§10.45
-
graphs Figure 10.26.10, Figure 10.26.10, Figure 10.26.10, Figure 10.26.7, Figure 10.26.7, Figure 10.26.7, Figure 10.26.8, Figure 10.26.8, Figure 10.26.8, Figure 10.26.9, Figure 10.26.9, Figure 10.26.9
-
limiting forms
§10.45
-
numerically satisfactory pairs
§10.45
-
tables
§10.75(viii)
-
uniform asymptotic expansions for large order
§10.45
-
zeros
§10.45
-
Poisson kernel for Laguerre polynomials
§18.18(vii)
-
power series
§10.31
-
principal branches (or values)
§10.25(ii)
-
recurrence relations
§10.29(i)
-
relations to other functions
-
sums
-
tables
§10.75(v)
-
Wronskians
§10.28
-
zeros
§10.42—§10.42
-
modified Bessel’s equation
§10.25(i)
-
modified Korteweg–de Vries equation
-
modified Mathieu functions Ch.28, see also radial Mathieu functions.
-
modified Mathieu’s equation
§28.20(i)
-
modified spherical Bessel functions, see spherical Bessel functions.
-
modified Struve functions, see Struve functions and modified Struve functions.
-
modified Struve’s equation, see Struve functions and modified Struve functions, differential equations.
-
modular equations
-
modular functions
§23.15
-
modular theorems
-
molecular spectra
-
molecular spectroscopy
-
mollified error
§3.1(v)
-
moments
§18.2(ix)
-
monic polynomial §1.11(ii), §3.5(v)
-
monodromy groups
-
monosplines
-
monotonicity
§1.4(i)
-
Monte Carlo methods
-
for multidimensional integrals
§3.5(x)
-
Monte Carlo sampling
§8.24(ii)
-
Mordell’s theorem
§23.20(ii)
-
Morse oscillator
§18.39(i)
-
Motzkin numbers
-
multidimensional theta functions, see Riemann theta functions and Riemann theta functions with characteristics.
-
multinomial coefficients
-
multiple orthogonal polynomials
§18.36(iii)
-
multiplicative functions
§27.3
-
multiplicative number theory
Ch.27—§27.12
-
multiplicity
-
multivalued function
§1.10(vi)
-
multivariate beta function
-
multivariate gamma function
-
multivariate hypergeometric function
§19.16(ii)—§19.16(ii)
-
mutual inductance of coaxial circles