Now, from the definition of k(m), given by equation (1.135), we find on setting n = 0, 1, 2, ..., and expanding k(0) = 1, %3D k(1) = k, %3D k(2) = k2 – k, | k(3) = k3 – 3k2 + 2k, (1.166) k(4) = k4 – 6k3+ 11k2 – 6k, k(5) = k5 – 10k4 + 35k3 – 50k2 + 24k, etc. These relations can be inverted to give the various powers of k in terms of the factorial functions 1 = k(0), k = k(1), k2 = k(2) + k(1), 3 = k(3) + 3k(2) + k(1), (1.167) k4 = k(4) + 7k(3) + 6k(2) + k(1), k5 = k(5) + 15k(4) + 25k(3) + 10k(2) + k(1), etc.
Now, from the definition of k(m), given by equation (1.135), we find on setting n = 0, 1, 2, ..., and expanding k(0) = 1, %3D k(1) = k, %3D k(2) = k2 – k, | k(3) = k3 – 3k2 + 2k, (1.166) k(4) = k4 – 6k3+ 11k2 – 6k, k(5) = k5 – 10k4 + 35k3 – 50k2 + 24k, etc. These relations can be inverted to give the various powers of k in terms of the factorial functions 1 = k(0), k = k(1), k2 = k(2) + k(1), 3 = k(3) + 3k(2) + k(1), (1.167) k4 = k(4) + 7k(3) + 6k(2) + k(1), k5 = k(5) + 15k(4) + 25k(3) + 10k(2) + k(1), etc.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
Related questions
Question
100%
Explain this and the definition from eq(1.35)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,