Abstract
By using some recently investigated fourier sine integral representations for the Mathieu type series (see [4]), new integral and series representations are derived here for certain general families of Mathieu type series.
Highlights
AND PRELIMINARIESThe following familiar infinite series (1.1) S (r) = +∞ n=1 (n2 2n + r2)2 r ∈R+is named after Emile Leonard Mathieu (1835-1890), who investigated it in his 1890 work [7] on elasticity of solid bodies
Several interesting problems and solutions dealing with integral representations and bounds for the following slight generalization of the Mathieu series with a fractional power
1 − x sin t 1 − 2x cos t + x2 dt
Summary
Fourier sine transforms, Bessel function, Gauss hypergeometric function, generalized hypergeometric function. Several interesting problems and solutions dealing with integral representations and bounds for the following slight generalization of the Mathieu series with a fractional power
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