The universe does end.............and it is expanding at an increasing rate..........for a good reason..........I think the primes end as well..............it is akin to why Einstein and others thought that the universe goes on forever.....................simply b/c u cannot see the edge.........................u cannot see how the earth curves......................etc..............and b/c people keep finding larger and larger primes.........they think they go on forever.........I doubt it.......................and the harmonic series increases to a big number...............with exponent of 1................but it is not infinite...........if it was in a race with the positive number line..........which goes up by ones.........whole numbers..........it would never catch up.........it cannot be infinite................

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In mathematics, the gamma function (represented by the capital Greek alphabet letter Γ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. That is, if n is a positive integer: Γ ( n ) = ( n − 1 ) ! . {\displaystyle \Gamma (n)=(n-1)!.}

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Gamma Function -- from Wolfram MathWorld

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by EW Weisstein - ‎2002 - ‎Cited by 40 - ‎Related articles

Gamma Function. The (complete) gamma function is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by. (1) ... The gamma function can be defined as a definite integral for (Euler's integral form)

‎Incomplete Gamma Function · ‎Digamma Function · ‎Log Gamma Function

Gamma function - Wikipedia

https://en.wikipedia.org/wiki/Gamma_function

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In mathematics, the gamma function (represented by the capital Greek alphabet letter Γ) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers. That is, if n is a positive integer: Γ ( n ) = ( n − 1 ) ! . {\displaystyle \Gamma (n)=(n-1)!.}

‎Improper integral · ‎Beta function · ‎Mellin transform · ‎Meromorphic function

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What is the value of gamma?

It has been proved that Γ(n + r) is a transcendental number and algebraically independent of π for any integer n and each of the fractions r = 16, 14, 13, 23, 34, 56. In general, when computing values of the gamma function, we must settle for numerical approximations.

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What is the zeta function?

Riemann zeta function, function useful in number theory for investigating properties of prime numbers. Written as ζ(x), it was originally defined as the infinite series ζ(x) = 1 + 2 ^−x + 3 ^−x + 4 ^−x + ⋯.When x = 1, this series is called the harmonic series, which increases without bound—i.e., its sum is infinite.

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What is the factorial of a number?

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5 ! = 5 × 4 × 3 × 2 × 1 = 120. {\displaystyle 5!=5\times 4\times 3\times 2\times 1=120.\ } The value of 0! is 1, according to the convention for an empty product.

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What is the error function?

In mathematics, the error function (also called the Gauss error function) is a special function (non-elementary) of sigmoid shape that occurs in probability, statistics, and partial differential equations describing diffusion. It is defined as: erf ⁡ ( x ) = 1 π ∫ − x x e − t 2 d t = 2 π ∫ 0 x e − t 2 d t .

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The Gamma Function - SOS Math

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Many important functions in applied sciences are defined via improper integrals. Maybe the most famous among them is the Gamma Function. This is why we ...

Gamma Function - Math

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(x) = (integral) (0 to inf) e ^-t t(x-1) dt. Gamma (x) = r ^x (integral) (0 to inf) e ^-rt t (x-1) dt. Gamma (x) = 2 (integral) (0 to inf) e (-t^2) t (2x-1) dt. ( Gamma (x) Gamma ...

[PDF]About the Gamma Function - University at Albany

www.albany.edu/~hammond/gellmu/examples/gamma.pdf

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by Γ Obviously - ‎Related articles

About the Gamma Function. Notes for Honors Calculus II,. Originally Prepared in Spring 1995. 1 Basic Facts about the Gamma Function. The Gamma function is ...