wow

2. By the group:

3. Jagadeesh.h

5. Born : 22 December 1887
Erode, Madras Presidency (now in Tamil Nadu)
Died : 26 April 1920 (aged 32)
Chetput, Madras, Madras Presidency (now Tamil Nadu)
Residence : Kumbakonam, Tamil Nadu
Academic advisors : G. H. Hardy
J. E. Littlewood
Known for : Landau–Ramanujan constat
Ramanujan conjecture
Ramanujan prime
Ramanujan–Soldner constant
Ramanujan theta function
Influences : G. H. Hardy
Signature :

6.  Ramanujan was born on 22 December 1887
in Erode,Madras(nowpalipalayam, erode, Tamil Nadu),
His father, K. Srinivasa Iyengar, worked as a
clerk in a sari shop and hailed from the district of tanjavur.
His mother, Komalatammal, was a housewifeand
also sang at a local temple.They lived in Sarangapani
Street in a traditional home in the town of Kumbakonam.
The family home is now a museum. When Ramanujan
was a year and a half old, his mother gave birth to a son
named Sadagopan, who died less than three months
later. In December 1889, Ramanujan had smallpox
and recovered, unlike thousands in the tanjavur. who
died from the disease that year.

7.  Ramanujan met deputy collector V. Ramaswamy
Aiyer, who had recently founded the Indian
Mathematical Society.
 Ramanujan, wishing for a job at the revenue
department where Ramaswamy Aiyer worked,
showed him his mathematics notebooks. As
Ramaswamy Aiyer later recalled:
I was struck by the extraordinary mathematical
results contained in it [the notebooks]. I had no
mind to smother his genius by an appointment in
the lowest rungs of the revenue department

8.  Rao and E.W.Middlemast tried to present
Ramanujan's work to British mathematicians.
One mathematician, M. J. M. Hill ofUniversity College
London, commented that Ramanujan's papers
were riddled with holes.
 He said that although Ramanujan had "a
taste for mathematics, and some ability",
he lacked the educational background and
foundation needed to be accepted by
mathematician. In the spring of 1913, Narayana Iyer,
Ramachandra

9.  He was invited England to improve his works by G.H. Hardy
and J.E. Littlewood,who were two of big mathematicans at thistime.
 Hardy and Ramanujan had two opposite personalities.As Hardy
was an atheist and believes mathematical proof and
analysis,Ramanujan was a deeply religious guy and
he believed in his trustworthy intuition.Hardy had hard
times on his education without giving any damage on
hisself confidence and his values.
 He was elected to the London Mathematical Society
and he became a Fellow of the Royal Society.

10. BACK TO INDIA
 Plagued by health problems throughout his life, living in a country
far away from home, and obsessively involved with his
mathematics, Ramanujan's health worsened in England, perhaps
exacerbated by stress and by the scarcity of vegetarian
food during the First World War. He was diagnosed
with tuberculosis and a severe vitamin deficiency and was
confined to a sanatorium.
 Ramanujan returned to Kumbakonam, Madras Presidency in
1919 and died soon thereafter at the age of 32 in 1920. His
widow, S. Janaki Ammal, moved to Mumbai, but returned to
Chennai (formerly Madras) in 1950, where she lived until her
death at age 94 in 1994.[28]
 A 1994 analysis of Ramanujan's medical records and symptoms
by Dr. D.A.B. Young concluded that it was much more likely he
had hepatic amoebiasis, a parasitic infection of the liver
widespread in Madras, where Ramanujan had spent time. He
had two episodes of dysentery before he left India. When not
properly treated, dysentery can lie dormant for years and lead to
hepatic amoebiasis,[76] a difficult disease to diagnose, but once
diagnosed readily cured.[76]

11.  Ramanujan has left a number of theorems and his notebooks
which have still been being worked on.
 Ramanujan found the mistery in the number,1729,while he was
in his bed when he was sick. Hardy was asked about 1729 what
he thought about it and he said it has nothing interesting.Then
Ramanujan stated that 1729 is the smallest number which could
be represented as in two different ways as a sum of two cubes.
After that,1729 have been called “Ramanujan-Hardy number”.
 According to the big mathematicians and specialists lived in
that time,Ramanujan’s talent was reminded them
Gauss,Jacobi,Euler.
 In memoriam of Ramanujan,books have been written and
movies were made since he died.An example could be the
movie named The Man Who Knew Infinity: A Life of the Genius
Ramanujan based on the book.

12.  In mathematics, there is a distinction between having
an insight and having a proof. Ramanujan's talent
suggested a plethora of formulae that could then be
investigated in depth later. It is said by G. H.
Hardy that Ramanujan's discoveries are unusually rich.
Examples of the most interesting of these formulae
include the intriguing infinite series for π, is given
below

13. OTHER VIEWS ABOUT
RAMANUJAN:
Hardy said :
“Ramanujan combined a power of generalization, a feeling for
form, and a capacity for rapid modification of his hypotheses, that were
often really startling, and made him, in his own peculiar field, without
a rival in his day. The limitations of his knowledge were as startling as
its profundity. Here was a man who could work out modular
equations and theorems... to orders unheard of, whose mastery of
continued fractions was... beyond that of any mathematician in the
world, who had found for himself the functional equation of the zeta
function and the dominant terms of many of the most famous
problems in the analytic theory of numbers; and yet he had never
heard of a doubly periodic function or ofCauchy's theorem, and had
indeed but the vaguest idea of what a function of a complex
variable was...".

14. Ramanujan's home state of Tamil Nadu celebrates 22
December (Ramanujan's birthday) as 'State IT Day',
memorialising both the man and his achievements, as a
native of Tamil Nadu.
A stamp picturing Ramanujan was released by the
Government of India in 1962 – the 75th anniversary of
Ramanujan's birth – commemorating his achievements in
number theory,[94] and a new design was issued on 26
December 2011, by the India Post

17. Hardy was also impressed by some of Ramanujan's
other work relating to infinite series of the following:

19.  The first notebook has 351 pages with 16 somewhat
organised chapters and some unorganised material.
 The second notebook has 256 pages in 21 chapters
and 100 unorganised pages
 The third notebook containing 33 unorganised
pages. The results in his notebooks inspired
numerous papers by later mathematicians trying to
prove what he had found. Hardy himself created
papers exploring material from Ramanujan's work as
did G. N. Watson, B. M. Wilson, and Bruce Berndt.
 A fourth notebook with 87 unorganised pages, the
so-called "lost notebook", was rediscovered in 1976
byGeorge Andrews.

22. Ramanujan theta function:
In mathematics, particularly q-analog theory,
the Ramanujan theta function generalizes the form
of the Jacobi theta functions, while capturing their
general properties. In particular, the Jacobi triple
product takes on a particularly elegant form when
written in terms of the Ramanujan theta. The
function is named after Srinivasa Ramanujan.
The Ramanujan theta function is used to
determine the critical dimensions in Bosonic String
Theory, Superstring Theoryand M-theory.

23. The Ramanujan theta function is defined as:
For |ab| < 1. The Jacobi tripleproduct identitythen takes the form

24. Page from Ramanujan's notebook
stating his Master theorem.
 In mathematics, Ramanujan's master theorem
(named after mathematicianSrinivasa Ramanujan)
is a techniquethat provides an analytic expression
for the Mellin transform of a function.
The result is stated as follows:
Assume function has an expansion of the form”
Then Mellin transform of is given by:
where is the Gamma function.
Ramanujan's master theorem

28. I had never seen anything in
the least like them before. A single
look at them is enough to show that
they could only be written by a
mathematician of the highest
class. They must be true
because, if they were not true, no
one would have the imagination to
invent them.
-Srinivasa Ramanujan