Mathematics for Enzyme Reaction Kinetics and Reactor Performance. F. Xavier MalcataЧитать онлайн книгу.
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after taking Eqs. (2.482) and (2.487) on board; the similarity of Eqs. (2.509) and (2.511) with Eqs. (2.469) and (2.471), respectively, is again striking – except for the minus, instead of plus sign.
2.4.2 Argument Transformation Formulae
Equation (2.472), pertaining to sinh x, may be multiplied by Eq. (2.473), pertaining to cosh y, to get
– in much the same way said equations were combined to produce Eq. (2.497) when y = x; after applying the distributive property of multiplication, Eq. (2.512) becomes
(2.513)
or, after recalling the rule of multiplication of exponential functions conveyed by Eq. (2.15),
Algebraic rearrangement permits transformation of Eq. (2.514) to
(2.515)
which is the same as writing
in view of the functional form of Eq. (2.472). A similar rationale may be applied to the product of sinh y by cosh x to get
(2.517)
again based on Eqs. (2.472) and (2.473) – where the two factors may be pooled together as
Eq. (2.518) may also appear as
After splitting its right‐hand side and factoring out −1 in selected exponents, Eq. (2.519) becomes
(2.520)
so Eq. (2.472) may again be invoked to write
in view of Eq. (2.475), one may redo Eq. (2.521) as
Ordered addition of Eqs. (2.516) and (2.522) gives rise to
(2.523)
which simplifies to
following condensation of terms alike – while ordered subtraction unfolds
(2.525)
with combination of terms alike leading to
Note the similarity of Eqs. (2.524) and (2.526) to Eqs. (2.328) and (2.330), respectively.
If Eq. (2.472) is multiplied by itself – using x and y at a time as arguments, one gets
(2.527)
in which case the two fractions may be collapsed to produce
Eq. (2.528) may be rewritten as
with the aid of Eq. (2.15). After splitting the right‐hand side, Eq.