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Connections between the iterated (anti)derivatives of es·x1/2 with respect to x and spherical modified Bessel functions of second kind
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November 11, 2014
Abstract
This paper investigates the underlying structure of the n-th derivative of es·x1/2 with respect to x. For n ∈ ℤ+, (dn/dxn)es·x1/2 can be expressed in terms of spherical modified Bessel functions of second kind in the complex plane. The representation holds for n ∈ ℤ-, where it represents the particular n-th antiderivative of es·x1/2 with all n constants of integration equal to zero. Our results introduce new connections among mathematical applications and provide some Bessel properties.
Received: 2013-7-14
Revised: 2014-3-13
Accepted: 2014-4-18
Published Online: 2014-11-11
Published in Print: 2014-12-1
© 2014 by De Gruyter
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Articles in the same Issue
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- Existence of positive solutions for a class of fractional differential equation systems with multi-point boundary conditions
- Two-quadratic modules and cofibration category
- Solutions of integro-differential equations related to contact problems of viscoelasticity
- Some Tauberian conditions obtained through weighted generator sequences
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- Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces
- The stability of some generalization of the quadratic functional equation
- A stability result of a Timoshenko system in thermoelasticity of second sound with a delay term in the internal feedback
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Keywords for this article
n-th derivative;
n-th antiderivative;
exponential function;
Bessel function
Articles in the same Issue
- Frontmatter
- Existence of positive solutions for a class of fractional differential equation systems with multi-point boundary conditions
- Two-quadratic modules and cofibration category
- Solutions of integro-differential equations related to contact problems of viscoelasticity
- Some Tauberian conditions obtained through weighted generator sequences
- On improvements of Opial-type inequalities
- Connections between the iterated (anti)derivatives of es·x1/2 with respect to x and spherical modified Bessel functions of second kind
- Analysis and approximation of frictionless contact problems between two piezoelectric bodies with adhesion
- Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces
- The stability of some generalization of the quadratic functional equation
- A stability result of a Timoshenko system in thermoelasticity of second sound with a delay term in the internal feedback
- An Ostrowski type inequality for derivatives of q-th power of s-convex functions via fractional integrals
- A new class of Tricomi–Legendre–Hermite and related polynomials
- A note on the norm convergence by Vilenkin–Fejér means
