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God made the natural numbers; all the rest is
the work of man. - Leopold
Kronecker
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The purpose of Series Math Study (SMS) website is to explore and develop the beauty of series formulas that have connections to special mathematical constants. Most of the series in this website are found with completed proofs. Some series can be used to calculate ever more accurate values of some special math constants as the desire that has challenged mathematicians for many centuries.
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I am
ashamed to tell you to how many figures I carried these computations,
having no other business at the time. |
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Issac Newton, personal
journal, 1666
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The
followings
are
outlines
and
brief
notes
of
the
series
formulas
that
have
been
developed
and
found
recently.
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August 03, 2010 |
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Two Series in Connection with Mathematical constants ·
·
or where
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July 03, 2010 |
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Sums in which the Square Root of Two and Other Constants Appear are Given by
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June 27, 2010 |
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A
Surprising Sum in which |
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April 18, 2010 |
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Some Special Infinite Series |
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·
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February 09, 2010 |
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Sums of Reciprocals of Two-Term Squares
Table |
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Sums of Reciprocals of Two-Term Cubes Table |
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January 30, 2010 |
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Series in Limit Form |
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Given n is a positive integer. The limits of the following series are found in a closed form as n tends to infinity.
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January 17, 2010 |
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Sequences and
Series Art -- A Generic Infinite Series Found Linking Three
Special Sequences '2, 30, 420, ...',
'15, 209, 2911, ...', and '17, 241, 3361, ...' with the Constant For any positive integer
where
and
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January 08, 2010 |
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Two
Beautiful Series in Connection with zeta ·
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January 01, 2010 |
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A Curious Series in Connection with Euler-Mascheroni, Pi Constants For positive integer n,
The above series can be transformed into another form, namely
Another curious series is found in connection to Pi
(Happy New Year
2010) |
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. 
,
is Riemann zeta function and
is 
. 
. 
. 
. 
Appears is
Given by 
.
.
.
,
are 
, 
,
,
,
.
and Pi Constants 
. 
. 
, where
is Euler-
.
.