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# umbral Sentence Examples

• For present purposes the form will be written a0x 1 +(7)a1x1=1 x2+ C 2)o'2x12 x 2 +...+anx2, the notation adopted by German writers; the literal coefficients have a rule placed over them to distinguish them from umbral coefficients which are introduced almost at once.

• As between the original and transformed quantic we have the umbral relations A1 = A1a1 d-A2a2, A2 = /21a1+/22a2, and for a second form B1 =A 1 b 1+ A 2 b 2, B 2 =/21bl +ï¿½2b2ï¿½ The original forms are ax, bi, and we may regard them either as different forms or as equivalent representations of the same form.

• This will be recognized as the resultant of the two linear forms. If the two linear forms be identical, the umbral sets a l, a2; b l, b 2 are alternative, are ultimately put equal to one another and (ab) vanishes.

• For present purposes the form will be written a0x 1 +(7)a1x1=1 x2+ C 2)o'2x12 x 2 +...+anx2, the notation adopted by German writers; the literal coefficients have a rule placed over them to distinguish them from umbral coefficients which are introduced almost at once.

• As between the original and transformed quantic we have the umbral relations A1 = A1a1 d-A2a2, A2 = /21a1+/22a2, and for a second form B1 =A 1 b 1+ A 2 b 2, B 2 =/21bl +Ã¯¿½2b2Ã¯¿½ The original forms are ax, bi, and we may regard them either as different forms or as equivalent representations of the same form.

• This will be recognized as the resultant of the two linear forms. If the two linear forms be identical, the umbral sets a l, a2; b l, b 2 are alternative, are ultimately put equal to one another and (ab) vanishes.