Golden Lemma and Golden pattern - Simplify everything right from polynomial multiplication, division , power , root , inverse - Help to build generic module in high level language to perform operation on polynomial - Parallel multiplication architecture for multiprocessor environment - Golden pattern(process) is applicable in many areas of algebra. - Golden pattern is superior over vertically crosswise pattern mentioned in Vedic math. To read more refer https://play.google.com/store/books/details/Vitthal_B_Jadhav_Modern_Approach_to_Speed_Math_Sec?id=PXi7jCVYClAC OR https://play.google.com/store/books/author?id=Vitthal+B.+Jadhav

1. 274 | Modern Approach to Speed Math Secret
3)
n
 
k 
 
n!

for n ∈ W , k ∈ W

k ! (n − k ) !


 n   n (n − 1) (n − 2) ..... (n − k + 1)

for n ∈ R , k ∈ W
 =
k 
k!
  


 n (n − 1) (n − 2) .... (k + 2) (k + 1) for n ∈ R , (n − k ) ∈ W

(n − k ) !

VJ’s GOLDEN LEMMA
Let k, l , m k , n ∈ W , Pk ∈ R
 mk
f ( x) = ∏  ∑ ak
k = 0 l = 0

n
,l
*x
Pk
mk −l 



Then
∞
f ( x) =
( Sl xh − l )
l =0
∑
Where
n
h = Highest power of x in f ( x) =
∑
ml pl
l =0
Pk 
 n
f ( x) 

 
U 0 =  ∏ ak , 0
 =  lim

h

 k =0
  x→∞ x


(
)
∪
Uk =
∀ al ,
r
present in U k −1
d
∫ dal , r (U k −1 ) dal , r + 1
r ≠ mi
Sl = Sum of all members ( terms) in set Ul =
∑ Ul
Golden Lemma / Golden Pattern
for k ≥ 1