SYMMETRY IDENTITIES OF CHANGHEE POLYNOMIALS OF&#x0D;
TYPE TWO

Jeong, Joohee; Kang, Dong-Jin; Rim, Seog-Hoon

doi:10.20944/preprints201810.0767.v1

Cited by 1 publication

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“…Recently, several authors studied the degenerate Bernoulli and degenerate Euler numbers and polynomials (see [1,2,4,5,7,9,10,11,12,13,14,15,16,17,18]). In addition, Jeong-Kang-Rim introduced symmetry identities for Changhee polynomials of type two closely related to type 2 degenerate Euler polynomials (see [6]), and Zhang and Lin obtained some interesting identities involving trigonometric functions and Bernoulli numbers (see [18]).…”

Section: Introductionmentioning

confidence: 99%

On type 2 degenerate Bernoulli and Euler polynomials of complex variable

et al. 2019

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Recently, Masjed-Jamei-Beyki-Koepf studied the so called new type Euler polynomials without making use of Euler polynomials of complex variable. Here we study degenerate and type 2 versions of these new type Euler polynomials, namely the type 2 degenerate cosine-Euler and type 2 degenerate sine-Euler polynomials and also the corresponding ones for Bernoulli polynomials, namely the type 2 degenerate cosine-Bernoulli and type 2 degenerate sine-Bernoulli polynomials by considering the degenerate Euler and degenerate Bernoulli polynomials of complex variable and by treating the real and imaginary parts separately. We derive some explicit expressions for those new polynomials and some identities relating to them. Here we note that the idea of separating the real and imaginary parts separately gives an affirmative answer to the question asked by Hacène Belbachir.2010 Mathematics Subject Classification. 11B83, 05A19. Key words and phrases. type 2 degenerate Bernoulli polynomials of complex variable, type 2 degenerate Euler polynomials of complex variable, type 2 degenerate cosine-Bernoulli polynomials, type 2 degenerate sine-Bernoulli polynomials, type 2 degenerate cosine-Euler polynomials, type 2 degenerate sine-Euler polynomials .

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