The simplest form of the κ and κ² order graviton self-interaction Lagrangian density in the weak field approximation

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We derive the simplest form of the κ(κ²) order graviton self-interaction Lagrangian density 1(2) in the weak field approximation. With the divergenceless condition, de Donder gauge and some combinatoric techniques, we derive the mathematically independent basis expressions for 1(2) composed of 8(24) terms. By using the basis expressions 1(2) is reduced to 6(18) terms.