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We discuss the partial infinite sum ∑∞ k=n u −s k for some positive integer n, where uk satisfies a recurrence relation of order s, un = aun−1 + un−2 + · · ·+ un−s (n ≥ s), with initial values u0 ≥ 0, uk ∈ N (0 ≤ k ≤ s− 1), where a and s(≥ 2) are positive integers. If a = 1, s = 2, and u0 = 0, u1 = 1, then uk = Fk is the k-th Fibonacci number. Our results… (More)

- Janyarak Tongsomporn, Vichian Laohakosol, Charinthip Hengkrawit, Patanee Udomkavanich
- J. Computational Applied Mathematics
- 2010

The stability of the functional equation F (x + y) − G(x − y) = 2H(x)K(y) over the domain of an abelian group G and the range of the complex field is investigated. Several related results extending a number of previously knownones, such as the ones dealingwith the sine functional equation, the d’Alembert functional equation and Wilson functional equation,… (More)

- Vichian Laohakosol, Pinthira Tangsupphathawat
- Discrete Applied Mathematics
- 2009

- Vichian Laohakosol, Nittiya Pabhapote
- Int. J. Math. Mathematical Sciences
- 2005

Rational arithmetic functions are arithmetic functions of the form g1 ∗···∗ gr ∗ h−1 1 ∗ ···∗h−1 s , where gi, hj are completely multiplicative functions and ∗ denotes the Dirichlet convolution. Four aspects of these functions are studied. First, some characterizations of such functions are established; second, possible Busche-Ramanujan-type identities are… (More)

- Vichian Laohakosol, Nittiya Pabhapote, NALINEE WECHWIRIYAKUL
- 2002

where α∈R, and n=∏p primepp denotes the prime factorization of n. This function is called the generalized Möbius function because μ1 = μ, the wellknownMöbius function. Note that μ0 = I, the identity functionwith respect to Dirichlet convolution, μ−1 = ζ, the arithmetic zeta function and μα+β = μα∗μβ; α, β being real numbers. Recall that an arithmetic… (More)

- Pakwan Riyapan, Vichian Laohakosol, Tuangrat Chaichana
- Periodica Mathematica Hungarica
- 2006

- Sui Sun Cheng, Sukrawan Talwong, Vichian Laohakosol
- Computing
- 2005

In general, it is difficult to compute explicit solutions for nonlinear differential equations. In this note, we show how power function solutions can be computed for a class of nonlinear functional equations involving derivatives and iterates of the unknown functions.

- Vichian Laohakosol, Nittiya Pabhapote
- Int. J. Math. Mathematical Sciences
- 2004

Given two multiplicative arithmetic functions, various conditions for their convolution, powers , and logarithms to be completely multiplicative, based on values at the primes, are derived together with their applications.

- Pattira Ruengsinsub, Vichian Laohakosol, Takao Komutsu, Sunanta Srisopha
- 2012

A necessary and sufficient condition for two arithmetic functions to be linearly dependent over the set of prime-free functions is derived. A new kind of convolution is introduced and an application is given.

- Vichian Laohakosol, Pattira Ruengsinsub, Nittiya Pabhapote
- Int. J. Math. Mathematical Sciences
- 2006

A generalized Ramanujan sum (GRS) is defined by replacing the usual Möbius function in the classical Ramanujan sum with the Souriau-Hsu-Möbius function. After collecting basic properties of a GRS, mostly containing existing ones, seven aspects of a GRS are studied. The first shows that the unique representation of even functions with respect to GRSs is… (More)