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and so on. Factorial of zero. The factorial of 0 is 1, or in symbols, 0! = 1.. There are several motivations for this definition: For n = 0, the definition of n! as a product involves the product of no numbers at all, and so is an example of the broader convention that the product of no factors is equal to the multiplicative identity (see Empty product). PDE (8) and BC (10), then c1u1 + c2u2 is also a solution, for any constants c1, c2. This relies on the linearity of the PDE and BCs. We will, of course, soon make this more precise.... Since each un (x,0) is a solution of the PDE, then the principle of superposition says any finite sum is also a solution. Texinfo Texinfo Copying Conditions 1 Overview of Texinfo 2 Writing a Texinfo File 3 Beginning and Ending a Texinfo File 4 Nodes 5 Chapter Structuring 6 Cross-references 7 Marking Text, Words and Phrases 8 Quotations and Examples 9 Lists and Tables 10 Special Displays 11 Indices 12 Special Insertions 13 Forcing and Preventing Breaks 14 Definition Commands 15 Internationalization 16 ...