DefinitionIntermediate
What is the recurrence relation for the gamma function as derived in this chapter?
The recurrence relation for the gamma function is given by Γ(x + 1) = xΓ(x). This can also be expressed as Γ(x) = (x - 1)Γ(x - 1).
Key points
- The gamma function is defined by the integral Γ(x) = ∫_0^∞ t^(x-1)e^(-t) dt for x > 0.
- The recurrence relation allows for the computation of the gamma function for integer values.
- For positive integers n, the relation simplifies to Γ(n + 1) = n! and Γ(n) = (n - 1)!
Advanced Engineering Mathematics
Stroud, K. A, Booth, Dexter J Stroud etc.
4th ed. · Industrial Press, Inc.