Functional Integrals for the Bogoliubov Gaussian Measure: Exact Asymptotic Forms

2018 ◽  
Vol 195 (2) ◽  
pp. 641-657
Author(s):  
V. R. Fatalov
Keyword(s):  
Gaussian Measure ◽  
Functional Integrals ◽  
Asymptotic Forms

STOCHASTIC AND OTHER FUNCTIONAL INTEGRALS

1990 ◽  
Vol 16 (2) ◽  
pp. 460 ◽  
Author(s):  
Henstock
Keyword(s):  
Functional Integrals

Application of functional integrals to stochastic equations

2017 ◽  
Vol 9 (3) ◽  
pp. 339-348 ◽  
Author(s):  
E. A. Ayryan ◽  
A. D. Egorov ◽  
D. S. Kulyabov ◽  
V. B. Malyutin ◽  
L. A. Sevastyanov
Keyword(s):  
Stochastic Equations ◽  
Functional Integrals

THE FUNCTIONAL INTEGRAL ON THE HALF-LINE

1990 ◽  
Vol 05 (15) ◽  
pp. 3029-3051 ◽  
Author(s):  
EDWARD FARHI ◽  
SAM GUTMANN
Keyword(s):  
Time Evolution ◽  
Wide Class ◽  
Green's Functions ◽  
Green’S Functions ◽  
Functional Integral ◽  
Half Line ◽  
Functional Integrals ◽  
Quantum Hamiltonian ◽  
Do So

A quantum Hamiltonian, defined on the half-line, will typically not lead to unitary time evolution unless the domain of the Hamiltonian is carefully specified. Different choices of the domain result in different Green’s functions. For a wide class of non-relativistic Hamiltonians we show how to define the functional integral on the half-line in a way which matches the various Green’s functions. To do so we analytically continue, in time, functional integrals constructed with real measures that give weight to paths on the half-line according to how much time they spend near the origin.

scholarly journals Asymptotic expansions of Lambert series and related q-series

2017 ◽  
Vol 13 (08) ◽  
pp. 2097-2113 ◽  
Author(s):  
Shubho Banerjee ◽  
Blake Wilkerson
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Expansions ◽  
Theta Functions ◽  
Lambert Series ◽  
Pochhammer Symbol ◽  
Complete Asymptotic Expansion ◽  
Polygamma Functions ◽  
Jacobi Theta Functions ◽  
Relative Errors ◽  
Asymptotic Forms

We study the Lambert series [Formula: see text], for all [Formula: see text]. We obtain the complete asymptotic expansion of [Formula: see text] near [Formula: see text]. Our analysis of the Lambert series yields the asymptotic forms for several related [Formula: see text]-series: the [Formula: see text]-gamma and [Formula: see text]-polygamma functions, the [Formula: see text]-Pochhammer symbol and the Jacobi theta functions. Some typical results include [Formula: see text] and [Formula: see text], with relative errors of order [Formula: see text] and [Formula: see text] respectively.

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