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Lerche–Newberger sum rule

Finds the sum of certain infinite series involving Bessel functions of the first kind From Wikipedia, the free encyclopedia

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The Lerche–Newberger, or Newberger, sum rule, discovered by B. S. Newberger in 1982,[1][2][3] finds the sum of certain infinite series involving Bessel functions Jα of the first kind. It states that if μ is any non-integer complex number, , and Re(α + β) > 1, then

Newberger's formula generalizes a formula of this type proven by Lerche in 1966; Newberger discovered it independently. Lerche's formula has γ =1; both extend a standard rule for the summation of Bessel functions, and are useful in plasma physics.[4][5][6][7]

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