“Lamé's Differential Equation”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lamé's Differential Equation

释义

Lamé's Differential Equation

(1)

(Byerly 1959, p. 255). The solution is denoted

and is known as a Lamé Function or anEllipsoidal Harmonic. Whittaker and Watson (1990, pp. 554-555) give the alternative forms

(2)

(3)

(4)

(5)

where

is a Weierstraß Elliptic Function and

			(6)
			(7)

			(8)

References

Byerly, W. E. An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, 1959.

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, 1990.

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