Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some new properties of Confluent Hypergeometric Functions   The confluent hypergeometric functions (the Kummer functions) defined by
${}_{1}F_{1}(\alpha;\gamma;z):=\sum_{n=0}^{\infty}\frac{(\alpha)_{n}}{n!(\gamma)_{n}}z^{n}\
(\gamma\neq 0,-1,-2,\cdots)$, which are of many properties and great
applications in statistics, mathematical physics, engineering and so on, have
been given. In this paper, we investigate some new properties of
${}_{1}F_{1}(\alpha;\gamma;z)$ from the perspective of value distribution
theory. Specifically, two different growth orders are obtained for $\alpha\in
\mathbb{Z}_{\leq 0}$ and $\alpha\not\in \mathbb{Z}_{\leq 0}$, which are
corresponding to the reduced case and non-degenerated case of
${}_{1}F_{1}(\alpha;\gamma;z)$. Moreover, we get an asymptotic estimation of
characteristic function $T(r,{}_{1}F_{1}(\alpha;\gamma;z))$ and a more precise
result of $m\left(r,
\frac{{}_{1}F_{1}'(\alpha;\gamma;z)}{{}_{1}F_{1}(\alpha;\gamma;z)}\right)$,
compared with the Logarithmic Derivative Lemma. Besides, the distribution of
zeros of the confluent hypergeometric functions is discussed. Finally, we show
how a confluent hypergeometric function and an entire function are uniquely
determined by their $c$-values.

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess