Goldstein%E2%80%99s
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1: 7.20 Mathematical Applications
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§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
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§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
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§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
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§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
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§7.2(ii) Dawson’s Integral
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7.2.5
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7.2.8
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, , and are entire functions of , as are and in the next subsection.
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6: 28.20 Definitions and Basic Properties
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§28.20(i) Modified Mathieu’s Equation
►When is replaced by , (28.2.1) becomes the modified Mathieu’s equation: ►
28.20.1
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28.20.2
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►For ,
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7: 22.16 Related Functions
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§22.16(ii) Jacobi’s Epsilon Function
►Integral Representations
… ►§22.16(iii) Jacobi’s Zeta Function
►Definition
… ►Properties
…8: 28.26 Asymptotic Approximations for Large
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§28.26(i) Goldstein’s Expansions
… ►Then as with fixed in and fixed , ►
28.26.4
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28.26.5
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►For additional terms see Goldstein (1927).
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9: 19.2 Definitions
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►Because is a polynomial, we have
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