“Elliptic Integral Singular Value k1”的概念、定义、习题解题方法及翻译-数学辞典

单词

Elliptic Integral Singular Value k1

释义

Elliptic Integral Singular Value k1

The first Singular Value , corresponding to

(1)

is given by

			(2)
			(3)

As shown in Lemniscate Function,


			(4)

Let

then


			(8)

where

is the Beta Function and

is the Gamma Function. Now use

(9)

and

(10)

(11)

Therefore,

(12)

Now consider

(13)

Let

Now note that

(18)

Now let

			(20)
			(21)

But

(26)


			(27)

Summarizing (12) and (27) gives

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