Difference between revisions of "Euler-Mascheroni constant"

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=References=
 
=References=
 
* {{BookReference|A course of modern analysis|1920|Edmund Taylor Whittaker|author2=George Neville Watson|edpage=Third edition|prev=Gamma|next=Reciprocal gamma written as an infinite product}}: $\S 12 \cdot 1$
 
* {{BookReference|A course of modern analysis|1920|Edmund Taylor Whittaker|author2=George Neville Watson|edpage=Third edition|prev=Gamma|next=Reciprocal gamma written as an infinite product}}: $\S 12 \cdot 1$
* {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Reciprocal gamma written as an infinite product|next=findme}}: §1.1 (4)
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* {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|prev=Reciprocal gamma written as an infinite product|next=findme}}: §1.1 (4)
 
* {{BookReference|Special Functions|1960|Earl David Rainville|prev=findme|next=Harmonic number}}: $7.(1)$
 
* {{BookReference|Special Functions|1960|Earl David Rainville|prev=findme|next=Harmonic number}}: $7.(1)$
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Limit of x^a log(x)=0|next=x/(1+x) < log(1+x)}}: $4.1.32$
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Limit of x^a log(x)=0|next=x/(1+x) less than log(1+x)}}: $4.1.32$
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Reciprocal gamma written as an infinite product|next=findme}}: 6.1.3
 
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Reciprocal gamma written as an infinite product|next=findme}}: 6.1.3

Latest revision as of 20:57, 3 March 2018

The Euler-Mascheroni constant is the number $\gamma$ defined by the formula $$\gamma = \lim_{n \rightarrow \infty} H_n-\log(n) = 0.577215664901532 \ldots,$$ where $H_n$ denotes the $n$th harmonic number.

Properties

The Euler-Mascheroni constant exists
Reciprocal gamma written as an infinite product
Exponential integral Ei series

Further properties

The Euler-Mascheroni constant appears in the definition of...

  1. the hyperbolic cosine integral
  2. the Barnes G function

See Also

Meissel-Mertens constant

External links

Collection of formulae for Euler's constant g

References