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n- 5. Use the Vandermonde identity to show that (²₁)-(:)(:1). k=0 Hint: Using central symmetry, write the Vandermonde identity in the form ("+")-((---) and substitute suitable m and 1. 2n k+m

n- 5. Use the Vandermonde identity to show that (²₁)-(:)(:1). k=0 Hint: Using central symmetry, write the Vandermonde identity in the form ("+")-((---) and substitute suitable m and 1. 2n k+m

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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n-1 2n · (²₁)-() (²). = 5. Use the Vandermonde identity to show that n- k=0 Hint: Using central symmetry, write the Vandermonde identity in the form m ("+") - (1) (+-) k+m k=0 (n+m+p and substitute suitable m and 1. 6. Give a counting argument for the three set version of the Vandermonde identity n (****)-Σ()()(-:-). k.j Р Hint: You need to count ways to choose / elements from the union of three disjoint sets with n, m and p elements. Split into cases where you choose k elements from the first and j elements from the second set.
Transcribed Image Text:n-1 2n · (²₁)-() (²). = 5. Use the Vandermonde identity to show that n- k=0 Hint: Using central symmetry, write the Vandermonde identity in the form m ("+") - (1) (+-) k+m k=0 (n+m+p and substitute suitable m and 1. 6. Give a counting argument for the three set version of the Vandermonde identity n (****)-Σ()()(-:-). k.j Р Hint: You need to count ways to choose / elements from the union of three disjoint sets with n, m and p elements. Split into cases where you choose k elements from the first and j elements from the second set.
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