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Number  theoretical  identities of  Er'Rahman,  which contain terms such as  {complex^complex }

Throughout  this page, the variable  (t)  is an integer.

Part-1a  and  Part-1b

These  identities  may be checked by a mathematica program, click  prg1a  or  prg1b  to see the program in txt format.  

Area of an ellipse with integer minor and major axis OR volume of an integer radius sphere  may also be evaluated similarly. By this method, we may express some of the fundamental formulas of classical geometry (with integer dimensions)  as  "pi-free"  expressions.

Part-2

This identity may be checked by a mathematica program, click  Prg2  to see the program in txt format.  

Part-3

This identity may be checked by a mathematica program, click  Prg3  to see the program in txt format.  

Part-4

This identity may be checked by a mathematica program, click  Prg4  to see the program in txt format.  

Part-5

This identity may be checked by a mathematica program, click  Prg5  to see the program in txt format. 

Part-6

This identity may be checked by a mathematica program, click  Prg6  to see the program in txt format. 

Part-7                                              (A serial addition form)

This identity may be checked by a mathematica program, click  Prg7  to see the program in txt format. 

Part-8                                              (A complex expression for  pi)

Combining   Part-5   by   Part-6  and referring  to  Part-1a,  we obtain an elegant expression for  pi,  in complex form.  

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