Formulas and Theorems for the Special Functions of Mathematical Physics
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The equivalence of the two representations of positive frequency functions for the Minkowski vacuum (2.14) and those for the Euclidean vacuum in the Milne universe (2.20) can be directly proven by using the formula [21,22].
“The equivalence of the two representations of positive frequency functions for the Minkowski vacuum (2.14) and those for the Euclidean vacuum in the Milne universe (2.20) can be directly proven by using the formula [21,22]”
From Quantized gravitational waves in the Milne universe (1997) · cites this paper as [22]
Cited by
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Singularity avoidance in a quantum model of the Mixmaster universe
Bergeron, H., Czuchry, E., Gazeau, J.-P., Małkiewicz, P., & Piechocki, W. (2015) · Physical Review D · doi:10.1103/physrevd.92.124018 · Cited by 37 · see citing works
Quantized gravitational waves in the Milne universe
Tanaka, T., & Sasaki, M. (1997) · Physical Review D · doi:10.1103/physrevd.55.6061 · Cited by 25 · see citing works
UWB signal processing: Projection, B-splines, and modified Gegenbauer bases
Casey, S. D., & Cohl, H. S. (2015) · 2015 International Conference on Sampling Theory and Applications (SampTA) · doi:10.1109/sampta.2015.7148840 · Cited by 7 · see citing works
Sampling architectures for ultra-wideband signals
Casey, S. D., & Cohl, H. S. (2017) · 2017 International Conference on Sampling Theory and Applications (SampTA) · doi:10.1109/sampta.2017.8024452 · Cited by 4 · see citing works
- Authors
- Magnus, W., Oberhettinger, F., & Soni, R. P.
- Venue
- Springer eBooks
- Publisher
- Springer Berlin Heidelberg
- Published
- 1966
- OpenAlex
- W1556192255
- Cited by
- 3,469
- References
- 0
- Citations by year
- 2026: 35 · 2025: 49 · 2024: 47 · 2023: 43 · 2022: 44 · 2021: 64 · 2020: 58 · 2019: 55 · 2018: 51 · 2017: 46 · 2016: 65 · 2015: 76 · 2014: 64 · 2013: 64 · 2012: 90
- FWCI
- 25.88
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Springer eBooks (publishedVersion)
- International Linear Collider (submittedVersion)
- Andalas University Repository (Andalas University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Keywords
- special functions, mathematical physics, formulas, theorems, mathematical tables
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
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