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Example of the optimal Kelly betting fraction, versus expected return of other fractional bets. In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a sequence of bets by maximizing the long-term expected value of the logarithm of wealth, which is equivalent to maximizing the long-term expected geometric growth rate.
Partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions ...
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: The first terms of the series sum to approximately , where is the natural logarithm and is the EulerโMascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
Unit fractions can also be expressed using negative exponents, as in 2 โ1, which represents 1/2, and 2 โ2, which represents 1/(2 2) or 1/4. A dyadic fraction is a common fraction in which the denominator is a power of two, e.g. โ 1 / 8 โ = โ 1 / 2 3 โ . In Unicode, precomposed fraction characters are in the Number Forms block.
The RogersโRamanujan continued fraction is a continued fraction discovered by Rogers (1894) and independently by Srinivasa Ramanujan, and closely related to the RogersโRamanujan identities. It can be evaluated explicitly for a broad class of values of its argument. Domain coloring representation of the convergent of the function , where is ...
The convergence of the geometric series with r=1/2 and a=1/2 The convergence of the geometric series with r=1/2 and a=1 Close-up view of the geometric series' partial sums over the range -1 < r < -0.5 as the first 11 terms of the geometric series 1 + r + r 2 + r 3 + ... are added, demonstrating alternating convergence.
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