Question

please show all steps, thanks

1. Find an explicit expression for P20). You may wish to involve the generating function "ſz, h) and make use of the binomial series (1 + x)" = 1+ ax + ala-1), ala - 1)(a - 2), ala-1)..(a - n+1). 21 n! Simplify your result by expressing Pe(0) in terms of two double factorials. Verify your result with the special cases l = 2,4,6.

Answer 1

Page Ans A& joren AlxA)e JI-axh th Let us toke IX0 then Ithi Now toke binomiaf expansion f (ItE) Ith2 22n 7-1 27 T .3. 5 On-) 2n (2n-1 (-I an #M

theore an -3 lo)h 27 (-1) othenwise. for n=2K for even For odd

Anea Date Page for l-a for le4 ( 3.1 4 (-1) (4-1)11 3 8 for le6 6-1)11 C-1) -6.५. २ 67 +6

ASD Date Page plo)= 3K 35x4-30x+3) fylD) = 3I0 f&lo) = -S 31x6-315x7 26 16 t/o 5x-5 Results ore vefied fe ,4.and 6