Exemple de utilizare a Gamma function în Engleză și traducerile lor în Română
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Support for gamma function.
The gamma function in the complex plane.
The absolute value of the Gamma function.
Where Γ(z) is the gamma function, a shifted generalization of the factorial function to non-integer values.
The function Γ("x") is the gamma function.
Where Γ is Leonhard Euler's gamma function(which can be thought of as an extension of the factorial function to fractional arguments).
Returns the natural logarithm of the gamma function, Γ(x).
Using explicit formulas for particular values of the gamma function at the integers and half integers gives formulas for the volume of a Euclidean ball that do not require an evaluation of the gamma function.
It is this extended version that is commonly referred to as the gamma function.
Returns the gamma function value.
Statistical: Returns the natural logarithm of the gamma function, Γ(x).
The following infinite product definitions for the gamma function, due to Euler and Weierstrass respectively, are valid for all complex numbers z, except the non-positive integers:: where is the Euler-Mascheroni constant.
And who claims he can give meaning to the negative values of the gamma function.
On the other hand, for integer order α,the following relationship is valid( note that the Gamma function becomes infinite for negative integer arguments):: this means that the two solutions are no longer linearly independent.
For integers n, Bern( x) has the series expansion:where is the Gamma function.
On the other hand, for integer order α,the following relationship is valid(note that the Gamma function has simple poles at each of the non-positive integers): :formula_3This means that the two solutions are no longer linearly independent.
Struve functions, denoted as have the following power series form:where is the gamma function.
The gamma function is a component in various probability-distribution functions, and as such it is applicable in the fields of probability and statistics, as well as combinatorics.
Power series expansion===Struve functions, denoted as have the following power series form:formula_2where is the gamma function.
In addition, Euler elaborated the theory of higher transcendental functions by introducing the gamma function and introduced a new method for solving quartic equations.
Alternative definitions===The following infinite product definitions for the gamma function, due to Euler and Weierstrass respectively, are valid for all complex numbers"t", except the non-positive integers: :formula_8where γ≈ 0.577216… is the Euler- Mascheroni constant.
In particular, it may be useful to have, in the set of antiderivatives, the special functions of physics(like the Legendre functions, the hypergeometric function, the Gamma function, the Incomplete Gamma function and so on- see Symbolic integration for more details).