Results 211 to 220 of about 12,516 (241)
Some of the next articles are maybe not open access.
Confluent hypergeometric functions
2010The details of the hypergeometric function were developed in Chapter 5. We used the notion\(F(\alpha,\beta ;\gamma ;z)\) to denote this function. A more complete notation on the hypergeometric function is\({}_2F_1 (\alpha,\beta ;\gamma ;z)\), which, in this chapter, is used in parallel with the shorter one.
openaire +2 more sources
The hypergeometric function, the confluent hypergeometric function and WKB solutions
Journal of the Mathematical Society of Japan, 2021Take the Gauss hypergeometric equation and instead of parameters \(a,b,c\) let us write \(a=\alpha_0+\alpha \eta, b=\beta_0+\beta\eta, c=\gamma_0+\gamma\eta\) and instead of the unknown function \(w\) let us take \(w=x^{-c/2}(1-x)^{(-1/2)(a+b-c+1)}\psi\). Then the equation is written in the form \[ (-\frac{d^2}{dx^2}+\eta^2Q)\psi=0,\quad Q=\sum_{j=0}^N
Aoki, Takashi +2 more
openaire +2 more sources
Geometric properties of $$\tau $$-confluent hypergeometric function
Analysis and Mathematical Physics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Deepak Bansal +2 more
openaire +2 more sources
The Confluent Hypergeometric Functions
200910.1 Introduction Whereas Gauss was largely responsible for the systematic study of the hypergeometric function, E. E. Kummer (1810â1893) is the person most associated with developing properties of the related confluent hypergeometric function. Kummer published his work on this function in 1836, and since that time it has been commonly referred to
openaire +1 more source
Univalence of confluent hypergeometric functions
1998Summary: Conditions of univalence and convexity for a confluent hypergeometric function \(\Phi\) with complex coefficients are obtained. Condition of starlikeness of \(z\Phi(z)\) is given.
Kanas, Stanisława, Stankiewicz, Jan
openaire +1 more source
The Confluent Hypergeometric Function
1991Many of the special functions of mathematical physics can be expressed in terms of specific forms of the confluent hypergeometric function. As its name suggests, this function is related to the hypergeometric function of Chapter 2. Let us see how.
openaire +1 more source
The Confluent Hypergeometric Functions
1998Abstract Whereas Gauss was largely responsible for the systematic study of the hypergeometric function, E. E. Kummer (1810-1893) is the person most associated with developing properties of the related confluent hypergeometric function.
openaire +1 more source
Confluent Hypergeometric Functions
Mathematics of Computation, 1961Y. L. L., L. J. Slater
openaire +2 more sources
The Confluent Hypergeometric Function Vol 15
Physics Bulletin, 1970H Buchholz Berlin: Springer 1969 pp xv + 238 price $16 The original German edition of this book appeared in 1953 as volume 2 of the Ergebnisse der Angewandten Mathematik. It contains virtually all the important information on confluent hypergeometric functions that was available at the time.
openaire +1 more source