Sharif, H. (2014). HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC. Algebraic Structures and Their Applications, 1(1), 23-33.

Habib Sharif. "HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC". Algebraic Structures and Their Applications, 1, 1, 2014, 23-33.

Sharif, H. (2014). 'HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC', Algebraic Structures and Their Applications, 1(1), pp. 23-33.

Sharif, H. HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC. Algebraic Structures and Their Applications, 2014; 1(1): 23-33.

HYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC

Let $K$ be a field of characteristic $p>0$, $K[[x]]$, the ring of formal power series over $ K$, $K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the field of rational functions over $K$. We shall give some characterizations of an algebraic function $f\in K((x))$ over $K$. Let $L$ be a field of characteristic zero. The power series $f\in L[[x]]$ is called differentially algebraic, if it satisfies a differential equation of the form $P(x, y, y',...)=0$, where $P$ is a non-trivial polynomial. This notion is defined over fields of characteristic zero and is not so significant over fields of characteristic $p>0$, since $f^{(p)}=0$. We shall define an analogue of the concept of a differentially algebraic power series over $K$ and we shall find some more related results.

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