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 LSTΧ
023 3 3 054 1 1 085 43 12 g LN
024 36 ENTER 055 7 7 086 43 36 g LSTΧ
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