H* function

== Definition ==
The H* function (defined by SuperJedi224 for generating new -illions) is defined as follows: Almost Infinite
*H*(m)=H(m)=103m+3
*H*(m,0)=m
*H*(m,n+1)=HH*(m,n)(m)=H(H(H(...H(m)...))), with H*(m,n) Hs.
*H*(a,...,b,c,1)=H*(a,...,b,c)
*H*(a,...,b,c,d)=H*(a,...,b,H*(a,...,b,c,d-1)) (Although the original definition does not clarify it, the rule is probably supposed to be applied only when d > 1).
In other words:
#If there is precisely one variable, the function value is the variable-th -illon.
#if there are precisely two variables:
##if the second variable is 0,the function value is the first variable.
##else:
###Decrease the second variable in 1, and call the new function value Z.
###The function value is recursion of the first variable through the H* function Z times.
#else:
##if the last entry is 1, remove it.
##else:
###Decrease the last variable by 1, and call the new function value Z.
###Replace the last two variables with one Z.
== Extended definition ==
The extended H* function (defined by SuperJedi224 for generating very large "-illions") is defined as follows:
*H*1(a)=H(a)=103a+3
*H*n(a,0)=a
*H*1(a,b)=H(H(H(...H(a)...))), with H*1(a,b-1) Hs.
*H*n(a,b)=H*n-1(a,a,...a,a) with H*n(a,b-1) "a"s.
*H*n(a,...,b,c,1)=H*n(a,...,b,c)
*H*n(a,...,b,c,d)=H*n(a,...,b,H*n(a,...,b,c,d-1))
== Examples ==
* H*(0) = 103 = 1,000 = thousand
* H*(1) = 106 = 1,000,000 = million
* H*(2) = 109 = 1,000,000,000 = billion
* H*(10) = 1033 = decillion
* H*(20) = 1063 = vigintillion
* H*(100) = 10303 = centillion
* H2(0) = H*(H*(0)) = H*(103) = millillion
* H2(1) = H*(H*(1)) = H*(106) = micrillion
* H2(2) = H*(H*(2)) = H*(109) = nanillion
* H2(10) = H*(H*(10)) = H*(1033) = mecillion
* H2(20) = H*(H*(20)) = H*(1063) = meicosillion
* H2(100) = H*(H*(100)) = H*(10303) = mehectillion
* H3(0) = H*(H*(H*(0))) = H*(H*(103)) = killamillillion
* H3(1) = H*(H*(H*(1))) = H*(H*(106)) = Killamicrillion
* H3(2) = H*(H*(H*(2))) = H*(H*(109)) = Killananillion
* H3(10) = H*(H*(H*(10))) = H*(H*(1033))
* H3(20) = H*(H*(H*(20))) = H*(H*(1063))
* H3(100) = H*(H*(H*(100))) = H*(H*(10303))
* H*(10,1) = HH*(10,0)(10) = H10(10) = H*(H*(H*(H*(H*(H*(H*(H*(H*(H*(10)))))))))) = hyperillion
* H*(20,1) = HH*(20,0)(20) = H20(20) = H*(H*(...H*(20)...)) (20 H's) = icosi-hyperillion
* H*(100,1) = HH*(100,0)(100) = H100(100) = H*(H*(...H*(100)...)) (100 H's) = cent-hyperillion
* H*(10,2) = HH*(10,1)(10) = HH10(10)(10) = H*(H*(...H*(10)...)) (hyperillion H's) = grand hyperillion
* H*(20,2) = HH*(20,1)(20) = HH20(20)(20) = H*(H*(...H*(20)...)) (icosi-hyperillion H's) = grand-icosi-hyperillion
* H*(10,3) = HH*(10,2)(10) = HHH10(10)(10)(10) = H*(H*(...H*(10)...)) (grand hyperillion H's) = bigrand hyperillion
* H*(20,3) = HH*(20,2)(10) = HHH20(20)(20)(20) = H*(H*(...H*(20)...)) (grand-icosi-hyperillion H's) = bigrand-icosi-hyperillion
* H*(10,4) = HH*(10,3)(10) = HHHH10(10)(10)(10)(10) = H*(H*(...H*(10)...)) (bigrand hyperillion H's) = trigrand hyperillion
* H*(10,10) = HH*(10,9)(10) = HHHHHHHHHH10(10)(10)(10)(10)(10)(10)(10)(10)(10)(10) = hyperduillion
* H*(10,10,2) = H*(10,H*(10,10)) = grand hyperduillion
* H*(10,10,3) = H*(10,H*(10,H*(10,10))) = bigrand hyperduillion
* H*(10,10,10) = H*(10,H*(10,...H*(10,10)...)) (10 H's) = hypertrillion
* H*(10,10,10,10) = H*(10,10,H*(10,10,...H*(10,10,10)...)) (10 H's) = hyperterillion
* H*(10,10,10,10,10) = H*(10,10,10,H*(10,10,10,...H*(10,10,10,10)...)) (10 H's) = hyperpetillion
* H*2(10,1) = H*(10,10,10,10,10,10,10,10,10,10) = H*(10,10,10,10,10,10,10,10,H*(10,10,10,10,10,10,10,10,...H*(10,10,10,10,10,10,10,10,10)...)) (10 H's) = hyperhypillion
* H*2(10,2) = H*(10,10,...,10,10) (hyperhypillion amount of tens) = grand hyperhypillion
* H*2(10,3) = H*(10,10,...,10,10) (grand hyperhypillion amount of tens) = bigrand hyperhypillion
* H*2(10,10) = great hyperhypillion
* H*2(100,100) = great cent-hyperhypillion
== Sources ==
Category:Functions
Category:Notations