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Bumped by Community user
added 186 characters in body; edited title
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qifeng618
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Is the hypergeometric function ${}_1F_2(1;a,a+\frac12;xa+\frac12;-x^2)$ an elementary function? How about its positivity, monotonicity, and convexity in $x$?

Is the generalized hypergeometric function ${}_1F_2\bigl(1;a,a+\frac12;x\bigr)$${}_1F_2\bigl(1;a,a+\frac12;-x^2\bigr)$ for $a>2$$a>-1$ and $x<0$$x>0$ an elementary function?

How about the positivity, monotonicity, and convexity of the generalized hypergeometric function ${}_1F_2\bigl(1; a, a+\frac{1}{2}; -x^2\bigr)$ in $x>0$ for $a\ge-1$?

Is the hypergeometric function ${}_1F_2(1;a,a+\frac12;x)$ an elementary function?

Is the hypergeometric function ${}_1F_2\bigl(1;a,a+\frac12;x\bigr)$ for $a>2$ and $x<0$ an elementary function?

Is the hypergeometric function ${}_1F_2(1;a,a+\frac12;-x^2)$ an elementary function? How about its positivity, monotonicity, and convexity in $x$?

Is the generalized hypergeometric function ${}_1F_2\bigl(1;a,a+\frac12;-x^2\bigr)$ for $a>-1$ and $x>0$ an elementary function?

How about the positivity, monotonicity, and convexity of the generalized hypergeometric function ${}_1F_2\bigl(1; a, a+\frac{1}{2}; -x^2\bigr)$ in $x>0$ for $a\ge-1$?

edited body; edited title
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qifeng618
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  • 14

Is the hypergeometric function ${}_1F_2(1,a1;a,a+\frac12;x)$ an elementary function?

Is the hypergeometric function ${}_1F_2\bigl(1,a,a+\frac12;x\bigr)$${}_1F_2\bigl(1;a,a+\frac12;x\bigr)$ for $a>2$ and $x<0$ an elementary function?

Is the hypergeometric function ${}_1F_2(1,a,a+\frac12;x)$ an elementary function?

Is the hypergeometric function ${}_1F_2\bigl(1,a,a+\frac12;x\bigr)$ for $a>2$ and $x<0$ an elementary function?

Is the hypergeometric function ${}_1F_2(1;a,a+\frac12;x)$ an elementary function?

Is the hypergeometric function ${}_1F_2\bigl(1;a,a+\frac12;x\bigr)$ for $a>2$ and $x<0$ an elementary function?

Source Link
qifeng618
  • 1.1k
  • 5
  • 14

Is the hypergeometric function ${}_1F_2(1,a,a+\frac12;x)$ an elementary function?

Is the hypergeometric function ${}_1F_2\bigl(1,a,a+\frac12;x\bigr)$ for $a>2$ and $x<0$ an elementary function?