# How to link value pairs to formula

I got this formula

lns[ri_, rj_, kij_, yi_, phm_, ylm_, plm_, yhm_, si_, ss_, sf_, mi_,
tsi_, δi_, dri_, drj_, lij_] =
10 Log[10^(-1 - #15 - #16 - #3 - #1/2 - #2/2 - 10 Log[5/2] -
10 Log[#9/10] - 10 Log[10/#10] - 10 Log[#10/#17] + (
10 Sqrt[#7/Sqrt[#6^2]] Log[(1000000000000 #5)/Sqrt[1/#8^2]])/
Sqrt[#5/Sqrt[1/#8^2]] -
10 Log[(Sqrt[#7/
Sqrt[#6^2]] (#4^2 + (#5 Sqrt[#6^2])/(#7 Sqrt[1/#8^2])))/(
Sqrt[#5/Sqrt[1/#8^2]] Sqrt[#4^2])] -
10 Log[(0.03344973747377862 10^(-1 - #1) #12)/(#13 #14)])]


Some values are frequency-dependent, so there are 21 different values ( 1 for each frequency ) I wrote them in Lists:

ri = {53, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21}
rj = {53, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21}
kij = {22, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21}
yi = {7, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21}
phm = {(10^-7), 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21}
ylm = {(-7), 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20, 21}
plm = {(10^-7), 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20, 21}
yhm = {14, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 21}

Δri = {0.008, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20, 21}
Δrj = {0.2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21}
Δkij = {0.2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21}
Δyi = {0.2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21}
Δphm = {(1 10^-9), 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21}
Δylm = {0.08, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15, 16, 17, 18, 19, 20, 21}
Δplm = {(1 10^-9), 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
13, 14, 15, 16, 17, 18, 19, 20, 21}
Δyhm = {0.2, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20, 21}

si = {7.37}
ss = {9.36}
sf = {7.52}
mi = {24}
tsi = {0.1, 1, 2, 3}
δi = {1}
dri = {1}
drj = {1}
lij = {1}

Δsi = {0.1}
Δss = {1}
Δsf = {1}
Δmi = {0.2}
Δtsi = {0.001}
Δδi = {0.01}
Δdri = {1}
Δdrj = {1}
Δlij = {0.01}


Last, there ist this calculation , which i want to do for every frequenz, (for every Part of the List)

How do I tell Mathematica to Put the Values of an exakt Spot in the List (here 1st) so ri=ri[[1]] and so on to the D[lns,phm] D[lns,ylm]... Funktions

Δlns50 = Sqrt[(
(D[lns, ri] Δri[[1]])^2 + (D[lns,
rj] Δrj[[1]])^2
+ (D[lns, kij] Δkij[[1]])^2 + (D[lns,
yi] Δyi[[1]])^2
+ (D[lns, phm] Δphm[[1]])^2 + (D[lns,
ylm] Δylm[[1]])^2
+ (D[lns, plm] Δplm[[1]])^2 + (D[lns,
yhm] Δyhm[[1]])^2
+ (D[lns, si] Δsi[[1]])^2 + (D[lns,
mi] Δmi[[1]])^2
+ (D[lns, tsi] Δtsi[[1]])^2 + (D[
lns, δi] Δδi[[1]])^2
+ (D[lns, lij] Δlij[[1]])^2)]


How do I tell Mathematica that all first Values of the List count, how do I tell Mathematica, to do the same calculation for the second, third,... 21st Part of teh List

so that I don't have to rewrite the calculation every time?

You should make a function:

rij=#1 /2 + dri + #2 /2 + drj + #3 + 10 Log[ss/(1 lij)]&


And further call it by rij[ri,rj,kij], substituting the desired values of ri, rj and kij which are associated with numbered slots for arguments (#1,#2,#3) of the function

If @Rom38's pure-function definition looks a bit esoteric, here's a more straightforward definition to the same effect:

rij[ri_, rj_, kij_] = ri/2 + dri + rj/2 + drj + kij + 10 Log[ss/(1 lij)];


Try it out:

rij[1, 2, 3]
(*    9/2 + dri + drj + 10 Log[ss/lij]    *)


Of course you'll have to define the other parameters (dri, drj, ss, lij`) as well.