Leonhard Euler Contribution

INTRODUCTION
Leonhard Euler was born on 1707, April 15 in Basel, Switzerland. He was a son of a famous Priest, Paul Euler. He died in 1783 St. Petersburg, Russia at the age of 76. Euler was a genius and born with a remarkable memory. Leonhard got his first education in mathematics at home from his dad, as his father was also interested in mathematics and studied from Jakob Bernoulli at university. At the age of 13 Euler entered the University of Basel and took courses from famous Professor, John Bernoulli, younger brother of Jakob Bernoulli. Euler was not limited to Mathematics; he also did Master’s degree in Philosophy. In 1727 he joined St. Petersburg Academy where he continued his research with Daniel Bernoulli in mechanics and physics and was able to publish his work in the respective field. Euler was dedicated to his work. He continued his scientific work even after losing sight in his right eye. Leonhard Euler was a great mathematician who, made exceptional

One of the Euler’s achievements of becoming famous was his solution of the “Basel problem”, the sum of the reciprocals of the squares. Euler found the sum of the infinite series + + ----------+ ------ = which was equal to and is known as Euler’s zeta function ς(s) for s=2 .
Euler was the first who gave f(x) as the notation to a function of x. In his book, “Introduction to the analysis of the infinite” he defined the exponential and logarithmic functions as limits, = By giving x the value one in the exponential series gives the Euler number e = 2.71828183…. In 1740 he discovered the universal Euler constant γ given by γ = ----------+ =0.577215665---- which gives the amazing relation between logarithmic function and harmonic