Can you have negative factorial

So this does not give you a definition of factorial for negative integers. Related questions What are continuous functions? What facts about continuous functions should be proved? Given two graphs of piecewise functions f x and g x , how do you know whether f[g x ] and See all questions in Continuous Functions. Impact of this question views around the world.

You can reuse this answer Creative Commons License. The factorials follow recurrence relations. Beta function on the real negative axis has also been redefined in the context of new concept.

Draw Function Graphs — Recheronline. Google Scholar. University of Waterloo, Waterloo. Goldbach, — In Memorium: Milton Abramowitz. Amer Math Monthly. Dutka J: The early history of factorial function. Arch Hist Exact Sci , 43 3 Article Google Scholar. SIAM Rev , 50 1 Gronau D: Why is the gamma function so as it is? Teach Math Comput Sci , 1: Ibrahim AM: Extension of factorial concept to negative numbers. Notes Theory Discrete Math , Lefort X: History of the logarithms: an example of the development of a concept in mathematics.

Cornell University. Book Google Scholar. Roman S: The logarithmic binomial formula. Amer Math Month , Srinivasan GK: The gamma function: An eclectic tour. Thukral AK: Logarithms of imaginary numbers in rectangular form: A new technique. Can J Pure Appl Sc , 8 3 Can J Pure Appl Sc , 8 2 Weistein EW: Factorial. Weistein EW: Double factorial.

Weistein EW: Beta function. Wikipedia: Factorial. Wikipedia: Double Factorial. Wikipedia: Beta function. Wolfram Research: Factorial. Wolfram Research: Gamma. Download references. You can also search for this author in PubMed Google Scholar. Correspondence to Ashwani K Thukral. Reprints and Permissions. Thukral, A. Factorials of real negative and imaginary numbers - A new perspective.

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Search all SpringerOpen articles Search. Download PDF. Background The factorial of a positive integer, n , is defined as, n! Figure 1. Full size image. Table 1 Roman factorials Full size table. Table 2 Factorials of some integers as per present concept Full size table. Figure 2. Table 3 Complex factorials of some real negative numbers Full size table. For positive integer indexes the rows sum to factorials, and even if the rows are interpolated to fractional indexes based on the closed-form-formula for the direct computation the rowsums are fractional factorials or gamma values.

Thus I assume the extension of the eulerian triangle to negative indexes gives the answer to a sensical definition of the factorials at negative parameters.

I have a more involved discussion in a hobby-treatize about the Eulerian-triangle here. My question was intended somewhat along the line: Assume the Gamma function is not yet invented and Goldbach asks you the question: "What is -n!

What would you answer? I will give my answer in this sens. What about saying the Bell numbers are the factorial numbers at negative integers? Is the answer encoded in one of the most important triangles in combinatorics? See what Knuth says about the origin of this duality table on page I am not sure why it should be a negative infinity.

Possibly because zero can be very small negative number as well as positive. I cannot derive the sign. But, I can prove that other integer negatives are also infinities. Sign up to join this community. The best answers are voted up and rise to the top. The factorial of -1, -2, -3, Ask Question. Asked 11 years, 10 months ago. Active 3 years, 8 months ago.

Viewed k times. So the question is: How could a sensible generalization of the factorial for negative integers look like? Improve this question. Bruce Arnold Bruce Arnold 1 1 gold badge 8 8 silver badges 14 14 bronze badges. When such an elementary question would be asked nowadays, it would get closed almost immediately.

In school we learned that factorial is like this: 3! I saw a comment on here asking if negative numbers could work like this: -3! It seems to me as a lay person that a simplification of the problem is to say that x!

From the mathematicians on here Just want to learn. They also seek things that are not just trivial extensions e.