Some integrals relating to the -function

Author:
Shigehiko Okui

Journal:
Math. Comp. **41** (1983), 613-622

MSC:
Primary 33A40; Secondary 94A05

DOI:
https://doi.org/10.1090/S0025-5718-1983-0717707-7

MathSciNet review:
717707

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Abstract: Various integrals relating to the -function

**[1]**S. O. Rice,*Statistical properties of a sine wave plus random noise*, Bell System Tech. J.**27**(1948), 109–157. MR**0023483**, https://doi.org/10.1002/j.1538-7305.1948.tb01334.x**[2]**Minoru Nakagami,*On the intensity distribution 2R\over√(𝛼𝛽)exp[-R^{2}\over2 (1\over𝛼+1\over𝛽)]I_{0} (R^{2}\over2[1\over𝛽-1\over𝛼]) and its application to signal statistics*, J. Res. Nat. Bur. Standards Sect. D**68D**(1964), 995–1003. MR**0165836****[3]**W. R. Bennett & J. R. Davey,*Data Transmission*, McGraw-Hill, New York, 1965.**[4]**S. Okui, N. Morinaga & T. Namekawa, "Statistical properties of maximal ratio combining diversity in correlated*m*-fading environments,"*Trans. IECE Japan*, v. 62-B, 1979, pp. 283-290.**[5]**F. Adachi, "Selection and scanning diversity effects in a digital FM land mobile radio with limiter discriminator detection,"*Trans. IECE Japan*, v. 64-E, 1981, pp. 398-405.**[6]**R. F. Pawula, S. O. Rice & J. H. Roberts, "Distribution of the phase angle between two vectors perturbed by Gaussian noise,"*IEEE Trans. Comm.*, v. COM-30, 1982, pp. 1828-1841.**[7]**A. Erdelyi et al. (ed.),*Higher Transcendental Functions*, Vols. 1-3, McGraw-Hill, New York, 1955.**[8]**A. Erdelyi et al. (ed.),*Tables of Integral Transforms*, Vols. 1 and 2, McGraw-Hill, New York, 1955.**[9]**I. S. Gradshteyn & I. M. Ryzhik,*Tables of Integrals, Series, and Products*, Corrected and enlarged edition, Academic Press, New York, 1980.**[10]**Yudell L. Luke,*Integrals of Bessel functions*, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1962. MR**0141801****[11]**F. A. J. Ford,*Some infinite integrals involving products of Bessel functions*, J. London Math. Soc.**41**(1966), 728–730. MR**0200493**, https://doi.org/10.1112/jlms/s1-41.1.728**[12]**William C. Lindsey,*Infinite integrals containing Bessel function products*, J. Soc. Indust. Appl. Math.**12**(1964), 458–464. MR**0167659****[13]**M. M. Agrest and M. S. Maksimov,*Theory of incomplete cylindrical functions and their applications*, Springer-Verlag, New York-Heidelberg, 1971. Translated from the Russian by H. E. Fettis, J. W. Goresh and D. A. Lee; Die Grundlehren der mathematischen Wissenschaften, Band 160. MR**0346209****[14]**Keith R. Lassey,*On the computation of certain integrals containing the modified Bessel function 𝐼₀(𝜉)*, Math. Comp.**39**(1982), no. 160, 625–637. MR**669654**, https://doi.org/10.1090/S0025-5718-1982-0669654-6**[15]**Fritz Oberhettinger and Larry Badii,*Tables of Laplace transforms*, Springer-Verlag, New York-Heidelberg, 1973. MR**0352889****[16]**A. H. Nuttall,*Some Integrals Involving the Q-Function*, NUSC Tech. Report 4297, 1972.**[17]**Shigehiko Okui,*Complete elliptic integrals resulting from infinite integrals of Bessel functions*, J. Res. Nat. Bur. Standards Sect. B**78B**(1974), 113–135. MR**0352566****[18]**Shigehiko Okui,*Complete elliptic integrals resulting from infinite integrals of Bessel functions. II*, J. Res. Nat. Bur. Standards Sect. B**79B**(1975), no. 3-4, 137–170. MR**0419888**

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0717707-7

Article copyright:
© Copyright 1983
American Mathematical Society