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]
References
^
Newberger, Barry S. (1982), "New sum rule for products of Bessel functions with application to plasma physics", J. Math. Phys., 23 (7): 1278–1281,
Bibcode:
1982JMP....23.1278N,
doi:
10.1063/1.525510.
^
Newberger, Barry S. (1983), "Erratum: New sum rule for products of Bessel functions with application to plasma physics [J. Math. Phys. 23, 1278 (1982)]", J. Math. Phys., 24 (8): 2250,
Bibcode:
1983JMP....24.2250N,
doi:10.1063/1.525940.
^
Bakker, M.; Temme, N. M. (1984), "Sum rule for products of Bessel functions: Comments on a paper by Newberger", J. Math. Phys., 25 (5): 1266,
Bibcode:
1984JMP....25.1266B,
doi:10.1063/1.526282.
^
Qin, Hong;
Phillips, Cynthia K.; Davidson, Ronald C. (2007), "A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions", Physics of Plasmas, 14 (9): 092103,
Bibcode:
2007PhPl...14i2103Q,
doi:
10.1063/1.2769968.
^
Lerche, I.; Schlickeiser, R.; Tautz, R. C. (2008), "Comment on "A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions" [Phys. Plasmas 14, 092103 (2007)]", Physics of Plasmas, 15 (2): 024701,
doi:10.1063/1.2839769.
^
Qin, Hong;
Phillips, Cynthia K.; Davidson, Ronald C. (2008), "Response to "Comment on 'A new derivation of the plasma susceptibility tensor for a hot magnetized plasma without infinite sums of products of Bessel functions'" [Phys. Plasmas 15, 024701 (2008)]", Physics of Plasmas, 15 (2): 024702,
doi:10.1063/1.2839770.