Lagrange's expansion formulaH-functionsThis paper gives a certain Laurent series expansion for a generalized Rodrigues type formula. The main result finds many applications which are enumerated briefly.doi:10.1007/BF02861836R.K. RainaSpringer India...
S. Bock On a three-dimensional analogue to the holomorphic z-powers: Laurent series ex- pansions. Complex Variables and Elliptic Equations, Vol. 57, 1271-1287 (2011).S. Bock, On a three-dimensional analogue to the holomorphic z-powers: power series and recurrence formulae, Complex Variables...
5) Laurent expansion Laurent展式 1. Laurent expansion and Liouville theorem of biregular function in Clifford analysis Clifford分析中双正则函数的Laurent展式和Liouville定理 2. In this paper, by using the Cauchy integral formula on certain distinguished boundary for functions with values in a ...
The expansion (2.35) is written as \begin{aligned} \wp (\phi _{z})&=\wp (\phi _{z}; \tau _q) = - \frac{1}{12} - \frac{z}{(1-z)^2} + 2 \sum _{n=1}^{\infty } \frac{q^{2n}}{(1-q^{2n})^2} -\sum _{n=1}^{\infty } \frac{n q^{2n}}{1-q^{2n}...
To find the Laurent Series of a function, you can use the Taylor Series expansion for the function centered at a point in its domain. This will give you the coefficients for the positive powers of the variable. To get the coefficients for the negative powers, you can use the Residue Theor...
q-Laurent expansionIn this article, Cauchy's integral formula for nth q-derivative of analytic functions is established and used to introduce a new proof to q-Taylor series by means of using the residue calculus in the complex analysis. Some theorems related to this formula are presented. A ...
Vice versa, iff∈ (D(z0,R)), then it has a power series expansion as above, called its 'Taylor series' (centred atz0). We will use this to show the general Cauchy Integral Formula, and to understand the nature of zeroes of holomorphic functions. Moreover, we will prove two ...
Laurent series expansionouter solid spherical monogenicsrecurrence formulaeThe main objective of this contribution is a constructive generalization of the holomorphic power and Laurent series expansions in to dimension three using the framework of hypercomplex function theory. This second article on hand ...
Laurent expansionand Liouville theorem of biregular function in Clifford analysis Clifford分析中双正则函数的Laurent展式和Liouville定理 2. In this paper, by using the Cauchy integral formula on certain distinguished boundary for functions with values in a universal Clifford algebra, theLaurent expansionfor...
5) expansion in laurent Laurent展开 例句>> 6) Laurent expansion Laurent展式 1. Laurent expansion and Liouville theorem of biregular function in Clifford analysis Clifford分析中双正则函数的Laurent展式和Liouville定理 2. In this paper, by using the Cauchy integral formula on certain distinguished...