Series Math Study
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 below or 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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(December 18, 2005)
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(December 7, 2005)
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, where 
is the Euler constant.
(November 12, 2005)
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(November 4, 2005)
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, where 
is
Riemann zeta function.
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, where constant e is the base of the natural
logarithm function.
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, where 
is Apéry’s
constant.
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, where G
is Catalan’s constant.
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, where 
is
Riemann zeta function.
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(August 26, 2005)
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(This series can be used to compute directly the n-th digit of ln(2) in base 6561 without computing any prior digits.)
(August 26, 2005)
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(This series can be used to compute directly the n-th digit of ln(3) in base 256 without computing any prior digits)
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, where 
.
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, where 
.
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, 0, 1 or
?
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