Using sigma summation notation the sum of the first m terms of the series can be expressed as :\sum_{n=1}^m n -1)^{n -1.
His notation is different from modern notation but can be constructed using more modern summation notation.
The notation (sum _{i in I}(prod _{m in A_{i}}m)=sum _{j in J}(prod _{m in B_{j}}m)) means that (sum _{i in I}(prod _{m in A_{i}}m)) and (sum _{j in J}(prod _{m in B_{j}}m)) are equivalent under relation R. Thus, the semantics they represent are equivalent.
This model can be combined with the model presented here by replacing the term that denotes substrate concentration and affinity for each ligand in [ 18] by the appropriate sum: in the notation employed by [ 18], this would mean replacing by for each ligand.
For this special notation, the sum or product of j running from 0 to S has S members, because the term with j = n is omitted.
Throughout the paper, we adopt the customary notation for the sum: where is an integer, is a positive integer and, " " denotes the function considered independently of whether it is defined for indicated arguments or not.
Throughout the paper, we adopt the customary notation for the sum: ∑ i = ℓ + s ℓ F ( i ) = 0, where ℓ is an integer, s is a positive integer and 'ℱ' denotes the function considered independently of whether it is defined for indicated arguments or not.
Utilizing a current notation, corresponding fractional sums of an appropriate function f can be written as ∇ q − γ a f ( q n a ) = ∑ k = 1 n ( 1 − q − 1 ) q k a ( q n a − q k − 1 a ) q ( γ − 1 ) Γ q − 1 f ( q k a ), n ∈ Z, γ > 0 (2).
To simplify the notation, I will indicate sums over i, a, b, as sums over ΔS.
Then if Vi = V for each i, the resulting direct sum can be written in exponential notation as V⊕N, or simply VN with the understanding that the direct sum is the default.
