A symmetric quantum calculus
  We introduce the $\alpha,\beta$-symmetric difference derivative and the $\alpha,\beta$-symmetric N\"orlund sum. The associated symmetric quantum calculus is developed, which can be seen as a generalization of the forward and backward $h$-calculus. 
Artur M. C. Brito da Cruz, Natalia Martins, Delfim F. M. Torres
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