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Tabulation of the function $ \psi(\theta)=\sum\sp \infty\sb {n=1}\sin n\theta/ n\sp 2$


Authors: A. Ashour and A. Sabri
Journal: Math. Comp. 10 (1956), 57-65
MSC: Primary 65.1X
DOI: https://doi.org/10.1090/S0025-5718-1956-0081003-8
MathSciNet review: 0081003
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  • [1] G. Källén, ``Mass- and charge-renormalization in quantum electrodynamics without use of the interaction representation,'' Arkiv f. Fysik, v. 2, 1950, p. 87-194; also, G. Källén & A. Sabry, ``Fourth order vacuum polarization,'' K. Danske videnskabernes selskab, Matematisk-Fysiske Medd., v. 29, no. 17, 1955. MR 0039581 (12:570a)
  • [2] Robert Karplus & Maurice Neuman, ``The scattering of light by light,'' Phys. Rev., v. 83, 1951, p. 776.
  • [3] See also W. Heitler, Quantum Theory of Radiation, 3rd Edition, Oxford Univ. Press, 1954, p. 252; R. Just, J. M. Luttinger, & M. Slotnick, ``Distribution of recoil nucleus in pair production by photons,'' Phys. Rev., v. 80, 1950, p. 189; G. Racah, ``Sopra L'irradiazione nell'urto di particelle veloci,'' p. 461-476; ``Sulla nascita dezli elettroni positivi,'' p. 477-481, Il Nuovo Cimento, S. 8, v. 11, 1934. MR 0041048 (12:786a)
  • [4] K. Mitchell, ``Tables of the function
    $\displaystyle \int_0^z {\frac{{ - \log \vert 1 - y\vert dy}}{y}} $
    , with an account of some properties of this and related functions,'' Phil. Mag., v. 40, 1949, p. 351-368. MR 0030294 (10:741a)
  • [5] E. E. Kummer, ``Über die Transcendenten, welche aus weiderholter Integratimen rationaler Formeln entstehen,'' J. f. d. reine u. angew. Math. (Crelle), v. 21, 1840, p. 47-90, 193-225.
  • [6] T. Clausen, ``Über die Zerlegung reeller gebrochener Funktionen,'' J. f. d. reine u. angew. Math. (Crelle), v. 8, 1832, p. 298-300.

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DOI: https://doi.org/10.1090/S0025-5718-1956-0081003-8
Article copyright: © Copyright 1956 American Mathematical Society

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