Transformations of Theta-3 and Theta-4 functions by using a new equation of four infinite series and sums built from a generalized recurrence relation

Motivated by the fundamental presence of mathematics in all engineering and scientific fields, this mathematical article is made in order to give a new important result about Theta functions. This is a mathematical article that starts by proving a recurrence relation that is very useful for the demonstrations of the present article. The article proves afterwards that four infinite series are equivalent and this result has been tested successfully on the softwares: GEOGEBRA and MATLAB. Consequently, new useful and simple transformations of Theta-3 and Theta-4 functions in their Nullwert forms have been proven. And thus, this article opens new opportunities to demonstrate and develop new mathematical findings and observations especially in the field of Theta Functions and Zeta Functions and the other related subjects.