Bernoulli polynomials using nested summations
Description
Posted by Namir in the MoHPC - HP Forum
Program calculates Bernoulli polynomials using nested summations (see Wikipedia).
Example 1:
5
ENTER
3.5
f A
output is 220.9375
Example 2:
3
ENTER
5.5
f A
output is 123.7500
Note: I was thinking about writing a second version of the listing for the HP-14C that uses the ISG command for registers 2 and 3. The problem is whenever the listing uses RCL 2 and RCL 3 it must be followed by the INT command. This adds more steps IMHO. So I abandoned the ISG-using version.
Program Resources
Labels
Storage Registers
Name |
Description |
|
0 |
x |
|
1 |
m |
|
2 |
n |
|
3 |
5 |
|
4 |
Bm(x) |
|
5 |
inner sum |
|
Program
Line |
Display |
Key Sequence |
|
Line |
Display |
Key Sequence |
|
000 |
|
|
|
024 |
45 3 |
RCL 3 |
|
001 |
42,21,11 |
f LBL A |
|
025 |
14 |
yˣ |
|
002 |
44 0 |
STO 0 |
|
026 |
20 |
× |
|
003 |
34 |
x↔y |
|
027 |
44,40, 5 |
STO + 5 |
|
004 |
44 1 |
STO 1 |
|
028 |
1 |
1 |
|
005 |
0 |
0 |
|
029 |
44,40, 3 |
STO + 3 |
|
006 |
44 2 |
STO 2 |
|
030 |
45 2 |
RCL 2 |
|
007 |
44 4 |
STO 4 |
|
031 |
45 3 |
RCL 3 |
|
008 |
42,21, 1 |
f LBL 1 |
|
032 |
43 10 |
g x≤y |
|
009 |
0 |
0 |
|
033 |
22 2 |
GTO 2 |
|
010 |
44 3 |
STO 3 |
|
034 |
45 5 |
RCL 5 |
|
011 |
44 5 |
STO 5 |
|
035 |
45 2 |
RCL 2 |
|
012 |
42,21, 2 |
f LBL 2 |
|
036 |
1 |
1 |
|
013 |
45 2 |
RCL 2 |
|
037 |
40 |
+ |
|
014 |
45 3 |
RCL 3 |
|
038 |
10 |
÷ |
|
015 |
43 40 |
g Cy,x |
|
039 |
44,40, 4 |
STO + 4 |
|
016 |
45 0 |
RCL 0 |
|
040 |
1 |
1 |
|
017 |
45 3 |
RCL 3 |
|
041 |
44,40, 2 |
STO + 2 |
|
018 |
40 |
+ |
|
042 |
45 1 |
RCL 1 |
|
019 |
45 1 |
RCL 1 |
|
043 |
45 2 |
RCL 2 |
|
020 |
14 |
yˣ |
|
044 |
43 10 |
g x≤y |
|
021 |
20 |
× |
|
045 |
22 1 |
GTO 1 |
|
022 |
1 |
1 |
|
046 |
45 4 |
RCL 4 |
|
023 |
16 |
CHS |
|
047 |
43 32 |
g RTN |
|