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One can then prove that this smoothed sum is asymptotic to − + 1 / 12 + CN 2, where C is a constant that depends on f. The constant term of the asymptotic expansion does not depend on f: it is necessarily the same value given by analytic continuation, − + 1 / 12 . [1]
The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...
That is, the digital sum is the same as the normal sum except that no carrying is used. For example, in decimal (base 10) arithmetic, the digital sum of 123 and 789 is 802: 3 + 9 = 12, discard the 10 leaving 2. 2 + 8 = 10, discard the 10 leaving 0. 1 + 7 = 8, there is no carry to discard. 123 789 --- 802
In mathematics, the digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045 {\displaystyle 9045} would be 9 + 0 + 4 + 5 = 18. {\displaystyle 9+0+4+5=18.}
The digit sum - add the digits of the representation of a number in a given base. For example, considering 84001 in base 10 the digit sum would be 8 + 4 + 0 + 0 + 1 = 13. The digital root - repeatedly apply the digit sum operation to the representation of a number in a given base until the outcome is a single digit. For example, considering ...
The additive persistence counts how many times we must sum its digits to arrive at its digital root. For example, the additive persistence of 2718 in base 10 is 2: first we find that 2 + 7 + 1 + 8 = 18, then that 1 + 8 = 9. There is no limit to the additive persistence of a number in a number base .
If only numbers with unique non-zero digits are considered, a three-digit number in base ten can have a digit-sum ranging from 6 = 1+2+3 to 24 = 7+8+9. If these potential digit-sums are used in the formula 2 x digit-sum x 11, the digit-sum of the result will determine whether or not the result is an Osiris number.
The ten digits of the Arabic numerals, in order of value. A numerical digit (often shortened to just digit) or numeral is a single symbol used alone (such as "1"), or in combinations (such as "15"), to represent numbers in positional notation, such as the common base 10. The name "digit" originates from the Latin digiti meaning fingers. [1]