Sentence examples for last identity from inspiring English sources

The last identity is Parseval's equality.

Note that the last identity owes to (19).

where the last identity holds because of (32).

where the last identity holds for the sake of (9).

where the last identity follows directly from the definition of the matrices.

end{aligned} Applying Theorem 2 to both sides of the last identity, we therefore establish the following transformation formula.

Substituting l − 1, x + 1, and ω − 1 q − l for l, n, and t in (4.3), respectively, we establish the last identities.

In this last case, the final identity of the mature functional tRNA-Ile depends on post-transcriptional modification of C-34 into an as yet unknown modified C-derivative (see below).

Taking the limit on each side of the last resulting identity as n → ∞, in view of (2.3), we obtain the following identity: ζ ( 2 r ) = ζ ( 2 r + 1 ) + ∑ j = 1 ∞ ∑ ℓ = 1 ∞ 1 ( ℓ + j ) 2 r + 1 ( r ∈ N ).

At last, the identity of the Beast is revealed, in all its majesty, while that of Stu, who has, perhaps unwisely, come as a plus one, is soon challenged: "Are you a demon?" "I'm a software analyst," he replies.

Since G p, i ( K ) = n W p, i ( K, T p, i K ) and W i ( K ) = W p, i ( K, K ), rewrite the last displayed identity as follows: W p, i ( K, T p, i K ) = W p, i ( K, [ W ˜ i ( K ∗ ) / ω n ] 1 / ( n − i ) K ).