Hills Equation Part I General Theory
Hills Equation Part I General Theory
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, But then, )9 •• (m^ ) ¥ and so, according to (2. 17), /\(m. ) / 0, which produces a contradiction. This proves Lemma 2. U in the case where /\ (X) ■ 2.
If ^ (X) « -2, the proof is almost literally the same. Incidentally, our proof of Lenima 2»U shows that the following is truei Lemma 2. S. The roots of the equation ^M - U - are either simple or double roots. If, for a particular value of X ■ ^l, (2. 22) ^i\x) - U, ^'(n) - 0, then^ (n) if ^- -2. Necessary and sufficient conditions for ^ (p. )... - U and ^ (^) to vanish simultaneously are (2. 23) y^^M - yi^M - yi[i\i) • yi^iik) - o, - 17 - In order to complete the proof of Theorem 2»1 we need Lcpgna 2>6» Let X be the smallest root of the equation /\ (X) - U ■ 0. Then X is a simple root and ^ (X ) 2 for X
What to read after Hills Equation Part I General Theory?
You can find similar books in the "Read Also" column, or choose other free books by W Magnus to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
, But then, )9 •• (m^ ) ¥ and so, according to (2. 17), /\(m. ) / 0, which produces a contradiction. This proves Lemma 2. U in the case where /\ (X) ■ 2.
If ^ (X) « -2, the proof is almost literally the same. Incidentally, our proof of Lenima 2»U shows that the following is truei Lemma 2. S. The roots of the equation ^M - U - are either simple or double roots. If, for a particular value of X ■ ^l, (2. 22) ^i\x) - U, ^'(n) - 0, then^ (n) if ^- -2. Necessary and sufficient conditions for ^ (p. )... - U and ^ (^) to vanish simultaneously are (2. 23) y^^M - yi^M - yi[i\i) • yi^iik) - o, - 17 - In order to complete the proof of Theorem 2»1 we need Lcpgna 2>6» Let X be the smallest root of the equation /\ (X) - U ■ 0. Then X is a simple root and ^ (X ) 2 for X
What to read after Hills Equation Part I General Theory?
You can find similar books in the "Read Also" column, or choose other free books by W Magnus to read onlineMoreLess
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