Identities for combinatorial sums involving trigonometric functions

• Type: Another Publication in an International Scientific Journal
• Date: 2023

Authors

Alzer, H (Author) Other; Yakubovich, SB (Author) FCUP

Journal

Title: Integral Transforms and Special Functions

Pages: 1-7

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 0 Citations

Scopus

Other information

Authenticus ID: P-00Y-07C

DOI: 10.1080/10652469.2023.2172004

Abstract (EN): LetA(m,n)(a) = sigma(m) (j=0) (-4)(j )(m + j 2j) sigma(n-1) (k=0)sin(a + 2k pi/n) cos(2j)(a + 2k pi/n)andB(m,n)(a) = sigma(m) (j=0) (-4)(j)(m + j +1 2j+1)sigma(n-1 ) (k=0 )sin(a + 2k pi/n)x cos(2j+1)(a + 2k pi/n),where m >= 0 and n >= 1 are integers and a is a real number. We present two proofs for the following results:(i) If 2m + 1 equivalent to 0 (mod n), thenA(m,n)(a) = (-1)(m)n sin((2m + 1)a).(ii) If 2m + 1 (sic) 0 (mod n), then A(m,n)(a) = 0.(iii) If 2(m + 1) equivalent to 0 (mod n), thenB(m,n)(a) = (-1)(m) n/2 sin(2(m + 1)a).(iv) If 2(m + 1) (sic) 0 (mod n), then B-m,B-n(a) = 0.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 7