Matematik Bölümünde 18.01.2016 tarihli seminer

18.01.2016

 

Fen Fakültesi toplantı salonunda 18 Ocak 2016 Pazartesi günü saat 11.00’de Bingöl Üniversitesi’nden Dr. Zafer Şiar tarafından “Some New Identities Concerning Horadam and its Companion Sequence by Matrix Method“ başlıklı İngilizce Matematik semineri verilmiştir.

 

Some New ·Identities concerning Horadam and its Companion Sequence by Matrix Method

Zafer ¸Siar

Bingöl University, Mathematics Department, Bingöl/TURKEY

zsiar@bingol.edu.tr

January 11, 2016

Abstract

In this study we will give a general relation between Horadam sequence

and the nxn matrices satisfying the relation X2 = PX + QI: Then we

will obtain some new identities between Horadam sequence fWng and its

companion sequence fXng using the 22 matrices X satisfying the rela-

tion X2 = PX +QI: Moreover, we will give some sum formulae including

the sequences fWng ; fXng ; fUng ; and fVng : Lastly, we we will give an

application of the sequences fWng and fXng to trigonometric functions,

which is some new angle addition formulas such as:

sin r sin(m + n + r) = sin(m + r) sin(n + r) 􀀀 sinm sin n;

cos r cos(m + n + r) = cos(m + r) cos(n + r) 􀀀 sinm sin n;

and

cos r sin(m + n) = cos(n + r) sinm + cos(m 􀀀 r) sin n:

References

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1

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and Lucas numbers, Hacettepe journal of Mathematics and Statistics, 42(3) (2013), 211-222.