Firstly, the definition of $k$-monogenic function with $\alpha$-weight in superspace is given and a series of properties of this function are discussed. Then the Cauchy-Pompeiu formula for $k$-monogenic function with $\alpha$-weight is obtained. Lastly, the Cauchy integral theorem for $k$-monogenic function with $\alpha$-weight is proved.
Zhiyuan FU
,
Heju YANG
,
Na XU
. CAUCHY INTEGRAL FORMULA FOR K-MONOGENIC FUNCTION WITH $\alpha$-WEIGHT IN SUPERSPACE[J]. Acta mathematica scientia, Series B, 2025
, 45(3)
: 825
-836
.
DOI: 10.1007/s10473-025-0305-5
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