“Hill Determinant”的概念、定义、习题解题方法及翻译-数学辞典

单词

Hill Determinant

释义

Hill Determinant

A Determinant which arises in the solution of the second-order Ordinary Differential Equation

(1)

Writing the solution as a Power Series

(2)

gives a Recurrence Relation

(3)

The value of

can be computed using the Hill determinant

(4)

where

and

is the variable to solve for. The determinant can be given explicitly by the amazing formula

(8)

where

(9)

leading to the implicit equation for ,

(10)

See also Hill's Differential Equation

References

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 555-562, 1953.

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