Skip to main content
Log in

Two-sided bounds uniform in the real argument and the index for modified Bessel functions

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

Bounds uniform in the real argument and the index for the functionsa ν (x)=xI′ ν (x)/I′ ν (x) andb ν (x)=xK′ ν (x)/K ν (x), as well as for the modified Bessel functionsI ν(x) andK ν(x), are established in the quadrantx>0, ν≥0, except for some neighborhoods of the pointx=0, ν=0.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. B. V. Pal’tsev, “On rapidly converging iteration methods with splitting of boundary conditions for a multidimensional Stokes type system. Periodic “flows” bounded by parallel walls,”Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.],325, No. 5, 926–931 (1992).

    Google Scholar 

  2. B. V. Pal’tsev, “On rapidly converging iteration methods with incomplete splitting of boundary conditions for a multidimensional singularly perturbed Stokes type system,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],185, No. 4, 101–150 (1994).

    Google Scholar 

  3. B. V. Pal’tsev, “On rapidly converging iteration methods with complete splitting of boundary conditions for a multi-dimensional singularly perturbed Stokes type system,”Mat. Sb. [Russian Acad. Sci. Sb. Math.],185, No. 9, 109–138 (1994).

    MATH  Google Scholar 

  4. A. A. Abramov and V. I. Ul’yanova, “On a method for solving a biharmonic type equation with a small parameter contained in a singular way,”Zh. Vychisl. Mat. i Mat. Fiz. [Comput. Math. and Math. Phys.],32, No. 4, 567–575 (1992).

    MathSciNet  Google Scholar 

  5. H. Bateman and A. Erdélyi,Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York-Toronto-London (1953).

    Google Scholar 

  6. M. Abramovich and I. Stigan,Reference Book for Special Functions [in Russian], Nauka, Moscow (1979).

    Google Scholar 

  7. G. Watson,A Treatise on the Theory of Bessel Functions, Pt. 1, Cambridge Univ. Press, Cambridge (1952).

    Google Scholar 

  8. F. W. J. Olver, “The asymptotic expansion of Bessel functions of large order,”Philos. Trans. Royal Soc. London. Ser. A,247, 328–368 (1954).

    Article  MathSciNet  Google Scholar 

  9. F. W. J. Olver,Asymptotics and Special Functions, Academic Press, New York-London (1974).

    Google Scholar 

  10. Ph. Hartman,Ordinary Differential Equations, New York (1967).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to B. V. Pal’tsev.

Additional information

Translated fromMatematicheskie Zametki, Vol. 65, No. 5, pp. 681–692, May, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pal’tsev, B.V. Two-sided bounds uniform in the real argument and the index for modified Bessel functions. Math Notes 65, 571–581 (1999). https://doi.org/10.1007/BF02743167

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02743167

Key words

Navigation