Nonextensive Statistical Mechanics

Appendix AUseful Mathematical Formulaeln q x ≡ x 1−q − 11 − q(x > 0, q ∈ R) (A.1)ln q x = x 1−q ln 2−q x (x > 0; ∀q) (A.2)ln q (1/x) + ln 2−q x = 0 (x > 0; ∀q) (A.3)q ln q x + ln (1/q) (1/x q ) = 0 (x > 0; ∀q) (A.4)e x q ≡ [1 + (1 − q) x] 11−q+ ≡⎧0 ifq < 1 and x < −1/(1 − q) ,⎪⎨⎪⎩[1 + (1 − q) x] 11−qif q < 1 and x ≥−1/(1 − q) ,e x if q = 1 (∀x) ,[1 + (1 − q) x] 11−qif q > 1 and x < 1/(q − 1) .(A.5)eq x e−x 2−q= 1 (∀q) (A.6)(eq x )q e −qx(1/q)= 1 (∀q) (A.7)e x+y+(1−q)xyq = e x q ey q (∀q) (A.8)329