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补充:
The book 'Special Functions' by Andrews, Askey and Roy.
page 253 All proofs are simple, easy to understand.
thm 5.4.1:Suppose that {Pn(x)} is a sequence of orthogonal polynomials w.r.t.
the distribution d\alpha(x) on the interval [a,b]. Then Pn(x) has n simple
zeros in [a,b].
remark: all roots are real. and no multiple roots. very very nice.
Thm 5.4.2 The zeros of Pn(x) and P_{n+1}(x) separate each other.
remark: in other words, the zeros interlace( 交错)
Thm 5.4.3 Let m |
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