Integrals whose saddle-point expansions terminate

Universal renormalization of saddle-point integrals for condensed Bose gases.

When treating the ground-state contribution exactly, a variant of the saddle-point method emerges that works even for condensed Bose gases. Results thus obtained, such as canonical partition functions, differ by universal renormalization factors from those provided by the conventional but incorrect scheme. The amended method yields the statistical properties of ideal and very weakly interacting...

Asymptotic Expansions for Integrals

SADDLE POINT VARIATIONAL METHOD FOR DIRAC CONFINEMENT

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...

Spi Multiplications of Oating Point Expansions Multiplications of Oating Point Expansions Multiplications of Oating Point Expansions

In modern computers, the oating point unit is the part of the processor delivering the highest computing power and getting all the attention from the design team. Performances of any multiple precision application will be dramatically enhanced by an adequate usage of the oating point expansions. We present in this work some new multiplication algorithms faster and more integrated than the stepw...

On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals—III: Clusters of saddle points

It is shown how the recently developed Hadamard expansion procedure can be applied to the hyperasymptotic evaluation of Laplace-type integrals containing a large variable when the phase function has a cluster of close-lying saddle points. Themodification to this procedure that is requiredwhen the saddles in the cluster coalesce to form a single higher-order saddle is discussed.An example is als...