The confluent hypergeometric functions M(a, b;z) and U(a, b;z) for large b and z
نویسندگان
چکیده
We obtain new and complete asymptotic expansions of the confluent hypergeometric functions M(a, b; z) and U(a, b; z) for large b and z. The expansions are different in the three different regions: z + a + 1 − b > 0, z + a + 1 − b < 0 and z + a + 1 − b = 0. The expansions are not of Poincaré type and we give explicit expressions for the terms of the expansions. In some cases, the expansions are valid for complex values of the variables too. We give numerical examples which show the accuracy of the expansions.
منابع مشابه
$k$-power centralizing and $k$-power skew-centralizing maps on triangular rings
Let $mathcal A$ and $mathcal B$ be unital rings, and $mathcal M$ be an $(mathcal A, mathcal B)$-bimodule, which is faithful as a left $mathcal A$-module and also as a right $mathcal B$-module. Let ${mathcal U}=mbox{rm Tri}(mathcal A, mathcal M, mathcal B)$ be the triangular ring and ${mathcal Z}({mathcal U})$ its center. Assume that $f:{mathcal U}rightarrow{mathcal U}$ is...
متن کاملOn modified asymptotic series involving confluent hypergeometric functions
A modification of standard Poincaré asymptotic expansions for functions defined by means of Laplace transforms is analyzed. This modification is based on an alternative power series expansion of the integrand, and the convergence properties are seen to be superior to those of the original asymptotic series. The resulting modified asymptotic expansion involves confluent hypergeometric functions ...
متن کاملParabolic starlike mappings of the unit ball $B^n$
Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...
متن کاملGeneralized Weighted Composition Operators From Logarithmic Bloch Type Spaces to $ n $'th Weighted Type Spaces
Let $ mathcal{H}(mathbb{D}) $ denote the space of analytic functions on the open unit disc $mathbb{D}$. For a weight $mu$ and a nonnegative integer $n$, the $n$'th weighted type space $ mathcal{W}_mu ^{(n)} $ is the space of all $fin mathcal{H}(mathbb{D}) $ such that $sup_{zin mathbb{D}}mu(z)left|f^{(n)}(z)right|begin{align*}left|f right|_{mathcal{W}_...
متن کاملIsomorphisms in unital $C^*$-algebras
It is shown that every almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Computational Applied Mathematics
دوره 233 شماره
صفحات -
تاریخ انتشار 2010