A new complex function space whose basis is the single-variable Hermite polynomial H-2j (xi*+tau xi/2 root tau) is constructed, which is related to both entangled state representation and spin coherent state in Schwinger bosonic realization. New binomial theorem involving two-variable Hermite polynomial is derived, which helps to constitute the new complex function space. We also present a new integration transformation of the basis H-2j (xi*+tau xi/2 root tau) with its reciprocal transformation which is useful to deriving some operator identities. (C) 2015 AIP Publishing LLC.
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机译：构造了一个新的复杂函数空间，其基础是单变量Hermite多项式H-2j（xi * + tau xi / 2根tau），它与Schwinger玻色子实现中的纠缠态表示和自旋相干态有关。推导了涉及二变量Hermite多项式的新二项式定理，它有助于构成新的复函数空间。我们还提出了基础H-2j（xi * + tau xi / 2 root tau）的新的积分变换及其对等变换，这对导出某些操作者身份很有用。 （C）2015 AIP Publishing LLC。
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