Relations involving scalar¶
Differentiations¶
N3∑k=1N2∑j=1N1∑i=1Tδξ1q=−N3∑k=1N2∑j=1((Tq)|12+N1+12∑i=12δξ1Tq−(Tq)|N1+12).
N3∑k=1N2∑j=1N1∑i=1Tδξ2q=−N3∑k=1N2−12∑j=12N1∑i=1δξ2Tq.
N3∑k=1N2∑j=1N1∑i=1Tδξ3q=−N3−12∑k=12N2∑j=1N1∑i=1δξ3Tq.
Averages¶
N3∑k=1N2∑j=1N1∑i=1T¯qξ1=N3∑k=1N2∑j=1(T|1q|122+N1−12∑i=32¯Tξ1q+T|N1q|N1+122).
N3∑k=1N2∑j=1N1∑i=1T¯qξ2=N3∑k=1N2−12∑j=12N1∑i=1¯Tξ2q.
N3∑k=1N2∑j=1N1∑i=1T¯qξ3=N3−12∑k=12N2∑j=1N1∑i=1¯Tξ3q.