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Adding short description: "Family of power series in mathematics" |
→The series 1F2: The removed text included a possible recursion relation suggested by a stack exchange question that 1. doesn't provide a result and 2. hadn't been answered. If there's a proposed relationship worthy of inclusion here, it should be proposed in a peer-reviewed paper. |
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The function <math>x\; {}_1F_2\left(\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{x^2}{4}\right)</math> is the antiderivative of the [[cardinal sine]]. With modified values of <math>a_1</math> and <math>b_1</math>, one obtains the antiderivative of <math>\sin(x^\beta)/x^\alpha</math>.<ref>Victor Nijimbere, Ural Math J vol 3(1) and https://arxiv.org/abs/1703.01907 (2017)</ref>
The function <math>{}_1F_2(1;a,a+1;x)</math> is essentially a [[Lommel function]].<ref>Watson's "Treatise on the Theory of Bessel functions" (1966), Section 10.7, Equation (10), according to https://mathoverflow.net/questions/98684</ref>
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