Applications of Volterra's theory of composition to hypergeometric functions

dc.contributor.author Wedel, Arnold
dc.contributor.department Mathematics
dc.date 2018-08-23T02:52:30.000
dc.date.accessioned 2020-06-30T07:24:32Z
dc.date.available 2020-06-30T07:24:32Z
dc.date.copyright Mon Jan 01 00:00:00 UTC 1951
dc.date.issued 1951
dc.description.abstract <p>The main results of this thesis are the generalizations of previous known results given by Hadamard (6), and Thielman (12) on integral addition theorems of Bessel functions, namely Theorems 5.8 and 5.9. Also an integral addition theorem, Theorem 5.10, for Laguerre polynomials is obtained;The methods used are based on the isomorphism which exists between Volterra's theory of permutable functions and the algebra of polynomials and power series. From known algebraic relations between certain given functions, integral addition theorems are obtained for new functions which are the Volterra transforms (see Definition 3.1) of the given functions. In particular recursion formulas for Tchebycheff polynomials lead to the integral addition theorems mentioned above;Other applications of the theory of composition are given, some of these lead to the evaluation of certain integrals and series expansions for hypergeometric functions. Identities concerning Tchebycheff polynomials are derived on the basis of the commutative property (see Definition 4.2) of these polynomials. Also an expression for a series involving triple products of Tchebycheff polynomials is obtained directly from the generating function of these polynomials. Since the Volterra transform of zp Tn(1 - 2z) is 2F2(n,-n;½,p;y - x), p > 0 some properties of the set of polynomials 2F2(n,-n;½,p;t), (n = 0,1,2,&mldr;), are obtained from these identities and theorems on Tchebycheff polynomials.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/12889/
dc.identifier.articleid 13888
dc.identifier.contextkey 6866444
dc.identifier.doi https://doi.org/10.31274/rtd-180813-14153
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/12889
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/66306
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/12889/r_DP11951.pdf|||Fri Jan 14 19:32:16 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Hypergeometric functions
dc.title Applications of Volterra's theory of composition to hypergeometric functions
dc.type dissertation
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
File
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
r_DP11951.pdf
Size:
2.97 MB
Format:
Adobe Portable Document Format
Description: