Neville%E2%80%99s
(0.004 seconds)
1—10 of 609 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
… ►Jacobi’s Elliptic Form
… ►Weierstrass’s Form
… ►§31.2(v) Heun’s Equation Automorphisms
… ►Composite Transformations
…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(iii) Floquet’s Theorem and the Characteristic Exponents
… ►This is the characteristic equation of Mathieu’s equation (28.2.1). … ►§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: 20.1 Special Notation
…
►
►
…
►Jacobi’s original notation: , , , , respectively, for , , , , where .
…
►Neville’s notation: , , , , respectively, for , , , , where again .
This notation simplifies the relationship of the theta functions to Jacobian elliptic functions (§22.2); see Neville (1951).
►McKean and Moll’s notation: , .
…
, | integers. |
---|---|
… | |
set of all elements of , modulo elements of . Thus two elements of are equivalent if they are both in and their difference is in . (For an example see §20.12(ii).) |
9: 19.2 Definitions
…
►Because is a polynomial, we have
…
►