Digitala Vetenskapliga Arkivet

Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
New transformation formulas for the fourth Lauricella function II
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.ORCID iD: 0000-0002-4687-1667
Uppsala Univ, Dept Math, POB 480, S-75106 Uppsala, Sweden..
2024 (English)In: Rendiconti del circolo matematico di Palermo, ISSN 0009-725X, E-ISSN 1973-4409, Vol. 73, no 8, p. 2921-2948Article in journal (Refereed) Published
Abstract [en]

In this our second article on the fourth Lauricella function, we start with some lemmas where Lauricella functions with m equal variables or with m copies of 1 can be reduced to a similar function. In the same way, Lauricella functions with m parameters equal to -1 can be reduced to a sum of Lauricella functions times elementary symmetric polynomials of the variables. These formulas are used in the proofs, as well as transformation formulas for Lauricella functions from the first paper. Our method gives a transformation with Kamp & eacute; de F & eacute;riet functions, which could possibly be extended. Also summation formulas for the first Appell function are proved. Because of the symmetric proofs, some q-analogues of these formulas can be found at the end of paper. All proofs use Eulerian (q-)integrals. Several formulas are generalizations of Kummer's second summation formula. In particular, the Euler-Pfaff transformation formula can be generalized to Lauricella functions. The sections are ordered according to the respective substitutions, and the recurring theme is again the reduced roots, which turn up as variables in the formulas. The power substitutions lead to formulas with complex function arguments, only one example is given.

Place, publisher, year, edition, pages
Springer Nature, 2024. Vol. 73, no 8, p. 2921-2948
Keywords [en]
Lauricella function, Appell function, Kampe de Feriet function, Reduction formula, (q-)Eulerian integral, Beta function
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-547722DOI: 10.1007/s12215-024-01057-9ISI: 001258599300001OAI: oai:DiVA.org:uu-547722DiVA, id: diva2:1937087
Funder
Uppsala UniversityAvailable from: 2025-02-12 Created: 2025-02-12 Last updated: 2025-02-12Bibliographically approved

Open Access in DiVA

fulltext(437 kB)26 downloads
File information
File name FULLTEXT01.pdfFile size 437 kBChecksum SHA-512
387470e816b56eaf061b3974bc61ab376cb76961110f88d1db0061d11c01375ec15c701aa9ddf3a69a94f7f5ca20d6ac763d1fda4639ed35c17aaaa5370a4226
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Ernst, Thomas
By organisation
Department of Mathematics
In the same journal
Rendiconti del circolo matematico di Palermo
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar
Total: 26 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 228 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf