Natural Log of Gamma Function (complex)

Description

This program computes the Natural Log of the Gamma Function for complex numbers.

Put a Complex number in the X register and press the A function key. (Computes the Ln of the Gamma Function of the complex number in X).

Note: Gamma of (6 + i0) is equivalent to 5 Factorial. So if you enter 6 then press A and ex the result will be 120 the same as 5 !.

This program is only accurate when the Real component is a positive number (between 0 and 70.9).

Program resources

Labels

Name Description
A Compute Ln of Gamma Function (complex)
1 Loop for continued fraction

Storage Registers

Name Description Name Description
0 Conversion Constant 1 6 Conversion Constant 7
1 Conversion Constant 2 7 Save Real Component
2 Conversion Constant 3 8 Save Imaginary Component
3 Conversion Constant 4 (i) Lookup of each Conversion Constant
4 Conversion Constant 5 I Index into conversion constants list
5 Conversion Constant 6

Flags

Number Description
8 Complex Mode

Program

Line Display Key Sequence Line Display Key Sequence Line Display Key Sequence
000    031 9   9 062 44 6   STO 6
001 42.21.11 f LBL A 032 5   5 063 45 7   RCL 7
002 44 7   STO 7 033 36   ENTER 064 45 8   RCL 8
003 42 30   f Re↔Im 034 3   3 065 42 25   f I
004 44 8   STO 8 035 7   7 066 6   6
005 43. 5. 8   g CF 8 036 1   1 067 44 25   STO I
006 43 35   g CLx 037 10   ÷ 068 34   x↔y
007 2   2 038 44 4   STO 4 069 36   ENTER
008 43 26   g π 039 1   1 070 36   ENTER
009 20   ✕ 040 48   . 071 36   ENTER
010 43 12   g LN 041 0   0 072 45 6   RCL 6
011 2   2 042 1   1 073 42.21. 1 f LBL 1
012 10   ÷ 043 1   1 074 40   ✛
013 44 0   STO 0 044 5   5 075 45 24   RCL (i)
014 1   1 045 2   2 076 34   x↔y
015 2   2 046 3   3 077 10   ÷
016 15   1/x 047 0   0 078 42. 5.25   f DSE I
017 44 1   STO 1 048 6   6 079 22 1   GTO 1
018 3   3 049 8   8 080 45 0   RCL 0
019 0   0 050 44 5   STO 5 081 40   ✛
020 15   1/x 051 1   1 082 34   x↔y
021 44 2   STO 2 052 48   . 083 30   −
022 5   5 053 5   5 084 43 36   g LSTx
023 3   3 054 1   1 085 43 12   g LN
024 36   ENTER 055 7   7 086 43 36   g LSTx
025 2   2 056 4   4 087 48   .
026 1   1 057 7   7 088 5   5
027 0   0 058 3   3 089 30   −
028 10   ÷ 059 6   6 090 20   ✕
029 44 3   STO 3 060 4   4 091 40   ✛
030 1   1 061 9   9 092 43 32 g RTN