a) of z is equal to b, square brackets, parenthesis, z divided by c sub m plus 2, close parenthesis, to the power m over m minus 1, minus 1, close square brackets;
b) of z is equal to b multiplied by the whole quantity: the quantity two plus z over c sub m, to the power m over m minus 1, minus 1.
the absolute value of the quantity sub j of t one, minus sub j of t two, is less than or equal to the absolute value of the quantity M of t one minus over j, minus M of t two minus over j.
k is equal to the maximum over j of the sum from i equals one to i equals n of the modulus of a sub i, j of t, where t lies in the closed interval a b and where j runs from one to n.
the limit as n becomes infinite of the integral of f of s and sub n of s plus delta n of s, with respect to s, from to t, is equal to the integral of f of s and of s, with respect to s, from to t.
sub n minus r sub s plus 1 of t is equal to p sub n minus r sub s plus 1, times e to the power t times sub q plus s.
L sub n adjoint of g is equal to minus 1 to the n, times the n -th derivative of a sub zero conjugate times g, plus, minus one to the n minus 1, times the n minus first derivative of a sub one conjugate times g, plus Е plus a sub n conjugate times g.
the partial derivative of F of lambda sub i of t and t, with respect to lambda, multiplied by lambda sub i prime of t, plus the partial derivative of F with arguments lambda sub i of t and t, with respect to t, is equal to 0.
the second derivative of y with respect to s, plus y, times the quantity 1 plus b of s, is equal to zero.
f of z is equal to phi sub mk hat, plus big O of one over the absolute value of z, as absolute z becomes infinite, with the argument of z equal to gamma.
D sub n minus 1 prime of x is equal to the product from s equal to zero to n of, parenthesis, 1 minus x sub s squared, close parenthesis, to the power epsilon minus 1.
K of t and x is equal to one over two pi i, times the integral of K of t and z, over omega minus omega of x, with respect to omega along curve of the modulus of omega minus one half, is equal to rho.
the second partial (derivative) of u with respect to t, plus a to the fourth power, times the Laplacian of the Laplacian of u, is equal to zero, where a is positive.
D sub k of x is equal to one over two pi i, times integral from c minus i infinity to c plus i infinity of dzeta to the k of omega, x to the omega divided by omega, with respect to omega, where c is grater than one.
The pronunciation of chemical words,
Formulae and equations
The modern trends are:
1. The accenting of names of chemical substances on the final syllable is notrecommended where the accent is not emphatic (such as the names amine [´æmaɪn], sulphide [´sʌlfaɪd], amidin [´æmɪdɪn]).
2. The general trend of the accent in the English language is now to be away from the end and toward the beginning of the word.
3. The ending Цide should be pronounced as [aɪd] (bromide [´broumaɪd], chloride [´klɔ:raɪd], oxide [´ɔksaɪd]).
4. For chemical names ending in Цine, the tendency is now to pronounce [i:n] (chlorine [´klɔ:ri:n], iodine [´aɪədi:n]).
This conflicts in sound with the pronunciation of the ending Ц ene but this is only with a few words, as benzine and benzene [´benzi:n], fluorine and fluorene [´fluəri:n], glycerinе [ɡlɪsə´ri:n].
5. The ending Цyl should be pronounced [ɪl] (methyl [´meθɪl]).
6. The ending Цile should be pronounced [ɪl] (nitrile [´naɪtrɪl]).
7. Adjectives ending in Ц ic should be accented on the next to the last syllable, as glyceric [ɡlɪ´serɪk].
8. Words ending in Ц valent [´veɪlənt] should be pronounced as trivalent [´traɪˌveɪlənt], monovalent [´mɔnouˌveɪlənt], divalent [´daɪˌveɪlənt] or bivalent [´baɪˌveɪlənt].