Sentence examples for real exponent from inspiring English sources

The Fourier transform of this intensity function is an exponential function with a real exponent.

The binomial theorem (1 + x n with an imaginary or real exponent is more general than with a positive integral exponent, but the former is considerably more complex and cannot be considered an objective ground of the latter which should be demonstrated first.

The q-analog of the power function ((a-b)^{(alpha)}) with real exponent (alphainmathbf{R}) is defined by (a-b)^{(alpha)}:=a^{alpha}prod_{n=0}^{infty}{ frac {1-(b/a)q^{n}}{1-(b/a)q^{n+alpha}}}, quad a,binmathbf{R}.

Since any irrational number can be expressed as the limit of a sequence of rational numbers, exponentiation of a positive real number b with an arbitrary real exponent x can be defined by continuity with the rule : b^x = \lim_{r (\in\mathbb Q \to x} b^r\quad(b \in\mathbb R^+,\,x\in\mathbb R) where the limit as r gets close to x is taken only over rational values of r.

So the same method working for real exponents also works for complex exponents.

However the identity :(b^r)^s = b^{r\cdot s} cannot be extended consistently to cases where b is a negative real number (see Real exponents with negative bases).

And so on for all of the infinitely many equivalent reformulations of the problem (in terms of the fourth, fifth, … power of the length, and indeed in terms of every non-zero real-valued exponent of the length).

The real number exponents g i,j and h i,j are kinetic orders that reflect the strength of the interactions from gene j to i.

For real trees, the exponent in the equation that describes Leonardo's hypothesis is not always equal to 2 but rather varies between 1.8 and 2.3 depending on the geometry of the specific species of tree.

In real systems the exponent γ is in the range between 2 and 3. Nodes of low connectivity are predominant in the network, whereas well-connected nodes are rare.

Here, polynomials with real values of exponents are introduced and used in forming mod traps, given a title 'fractional polynomial mod trap' (FPMT).