What question did this study set out to answer?

To establish analytical techniques for evaluating multidimensional infinite series representing planar lattice sums in terms of known special functions.

March 1, 1973Journal of Mathematical Physics

The evaluation of lattice sums. I. Analytic procedures

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Authors

MGM. L. GlasserUniversidad de Valladolid

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Implication

Theoretical analysis demonstrates exact analytic summation methods in planar lattice geometries, indicating direct evaluation through zeta and related functions.

Key Points

To establish analytical techniques for evaluating multidimensional infinite series representing planar lattice sums in terms of known special functions.
Formulated mathematical procedures to sum infinite multidimensional series containing quadratic forms of the type (i^2 + j^2 + k^2 + ...)^(-s).
Applied algebraic transformations to express planar lattice configurations using zeta functions and related analytic formulations.
Derived exact analytical formulations that evaluate complex planar lattice sums directly in terms of the Riemann zeta and related functions.
Provided systematic reduction methods for multidimensional infinite series without requiring numerical approximations.

Cite This Study

M. L. Glasser (1973) studied this question.

synapsesocial.com/papers/6a93c2ef80e39a190d56c26b https://doi.org/10.1063/1.1666331

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Implication

Theoretical analysis demonstrates exact analytic summation methods in planar lattice geometries, indicating direct evaluation through zeta and related functions.

The evaluation of lattice sums. I. Analytic procedures

Discussion

Member takes

Implication

Key Points

Cite This Study

The evaluation of lattice sums. I. Analytic procedures

Discussion

Member takes

Implication

Key Points

Cite This Study

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