The Logarithmic Solutions of the Hypergeometric Equation
Author: Niels Erik Nørlund
Publisher:
Published: 1963
Total Pages: 66
ISBN-13:
DOWNLOAD EBOOKRead and Download eBook Full
Author: Niels Erik Nørlund
Publisher:
Published: 1963
Total Pages: 66
ISBN-13:
DOWNLOAD EBOOKAuthor: Niels Erik Nörlund
Publisher:
Published: 1963
Total Pages: 58
ISBN-13:
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 1963
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKAuthor: Niels Erik Nörlund
Publisher:
Published: 1963
Total Pages: 58
ISBN-13:
DOWNLOAD EBOOKAuthor: N. E. Nörlund
Publisher:
Published: 1963
Total Pages: 58
ISBN-13:
DOWNLOAD EBOOKAuthor: Michihiko Matsuda
Publisher:
Published: 1985
Total Pages: 138
ISBN-13:
DOWNLOAD EBOOKAuthor: Lyle E. Mehlenbacher
Publisher:
Published: 1936
Total Pages: 28
ISBN-13:
DOWNLOAD EBOOKAuthor: Herbert Buchholz
Publisher: Springer Science & Business Media
Published: 2013-11-22
Total Pages: 255
ISBN-13: 3642883966
DOWNLOAD EBOOKThe subject of this book is the higher transcendental function known as the confluent hypergeometric function. In the last two decades this function has taken on an ever increasing significance because of its use in the application of mathematics to physical and technical problems. There is no doubt that this trend will continue until the general theory of confluent hypergeometric functions becomes familiar to the majority of physicists in much the same way as the cylinder functions, which were previously less well known, are now used in many engineering and physical problems. This book is intended to further this development. The important practical significance of the functions which are treated hardly demands an involved discussion since they include, as special cases, a number of simpler special functions which have long been the everyday tool of the physicist. It is sufficient to mention that these include, among others, the logarithmic integral, the integral sine and cosine, the error integral, the Fresnel integral, the cylinder functions and the cylinder function in parabolic cylindrical coordinates. For anyone who puts forth the effort to study the confluent hypergeometric function in more detail there is the inestimable advantage of being able to understand the properties of other functions derivable from it. This gen eral point of view is particularly useful in connection with series ex pansions valid for values of the argument near zero or infinity and in connection with the various integral representations.
Author: Yoshihiro Takeyama
Publisher:
Published: 2001
Total Pages: 9
ISBN-13:
DOWNLOAD EBOOKAbstract: "We consider the q-hypergeometric equation with q[superscript N] = 1 and [alpha], [beta], [gamma] [element of] Z. We solve this equation on the space of functions given by a power series multiplied by a power of the logarithmic function. We prove that the subspace of solutions is two-dimentional [sic] over the field of quasi-constants. We get a basis for this space explicitly. In terms of this basis, we represent the q-hypergeometric function of the Barnes type constructed by Nishizawa and Ueno. Then we see that this function has logarithmic singularity at the origin. This is a difference between the q-hypergeometric functions with 0
Author: Marvin E. Goldstein
Publisher:
Published: 1973
Total Pages: 364
ISBN-13:
DOWNLOAD EBOOKThis book is based on a course presented at the Lewis Research Center for engineers and scientists who were interested in increasing their knowledge of differential equations. Those results which can actually be used to solve equations are therefore emphasized; and detailed proofs of theorems are, for the most part, omitted. However, the conclusions of the theorems are stated in a precise manner, and enough references are given so that the interested reader can find the steps of the proofs.