Number of Terms in Homogeneous Polynomial
Jump to navigation
Jump to search
Theorem
The number of terms in a homogeneous polynomial of degree $n$ in $m$ indeterminates is given by:
- $N = \dbinom {n + m - 1} n = \dfrac {\paren {n + m - 1}!}{n! \, \paren {m - 1}!}$
Proof
This theorem requires a proof. In particular: By induction, probably, but really need to rationalise the existing material on polynomials You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |
Sources
- 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 1$. Introduction: Exercise $12$