Barrett’s
(0.002 seconds)
1—10 of 602 matching pages
1: 7.20 Mathematical Applications
…
►
§7.20(ii) Cornu’s Spiral
►Let the set be defined by , , . Then the set is called Cornu’s spiral: it is the projection of the corkscrew on the -plane. … ► …2: 31.2 Differential Equations
…
►
§31.2(i) Heun’s Equation
►
31.2.1
.
…
►
Jacobi’s Elliptic Form
… ►Weierstrass’s Form
… ►§31.2(v) Heun’s Equation Automorphisms
…3: 29.2 Differential Equations
…
►
§29.2(i) Lamé’s Equation
… ►§29.2(ii) Other Forms
… ►we have …For the Weierstrass function see §23.2(ii). … ►4: 28.2 Definitions and Basic Properties
…
►
§28.2(i) Mathieu’s Equation
… ►
28.2.1
…
►
§28.2(iii) Floquet’s Theorem and the Characteristic Exponents
… ►§28.2(iv) Floquet Solutions
… ► …5: 7.2 Definitions
…
►
…
§7.2(ii) Dawson’s Integral
►
7.2.5
…
►
7.2.8
►
, , and are entire functions of , as are and in the next subsection.
…
►
6: 28.20 Definitions and Basic Properties
…
►
§28.20(i) Modified Mathieu’s Equation
►When is replaced by , (28.2.1) becomes the modified Mathieu’s equation: ►
28.20.1
…
►
28.20.2
.
…
►For ,
…
7: 22.16 Related Functions
…
►
§22.16(ii) Jacobi’s Epsilon Function
►Integral Representations
… ►§22.16(iii) Jacobi’s Zeta Function
►Definition
… ►Properties
…8: 19.2 Definitions
…
►Because is a polynomial, we have
…
►
§19.2(ii) Legendre’s Integrals
… ►Legendre’s complementary complete elliptic integrals are defined via … ►§19.2(iii) Bulirsch’s Integrals
►Bulirsch’s integrals are linear combinations of Legendre’s integrals that are chosen to facilitate computational application of Bartky’s transformation (Bartky (1938)). …9: 28.8 Asymptotic Expansions for Large
…
►
§28.8(iii) Goldstein’s Expansions
… ►Barrett’s Expansions
►Barrett (1981) supplies asymptotic approximations for numerically satisfactory pairs of solutions of both Mathieu’s equation (28.2.1) and the modified Mathieu equation (28.20.1). … ►Dunster’s Approximations
… ►10: Bibliography B
…
►
Tables of modified Struve functions of orders zero and unity.
►
Mathieu functions of general order: Connection formulae, base functions and asymptotic formulae. I–V.
Philos. Trans. Roy. Soc. London Ser. A 301, pp. 75–162.
…
►
Ramanujan’s Notebooks. Part II.
Springer-Verlag, New York.
►
Ramanujan’s Notebooks. Part III.
Springer-Verlag, Berlin-New York.
…
►
Waves and Thom’s theorem.
Advances in Physics 25 (1), pp. 1–26.
…