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I have trouble evaluating the following generalised hypergeometric function:

HypergeometricPFQRegularized[{1/2, 1, n/2}, {1 - m, 1 + m}, x]

at certain values of $n,m,x$. The Mathematica guide states that the result ought to be finite for all (finite) values of $n,m,x$.

However, attempting to evaluate:

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5, 1 + 1.5}, 0.9]

and Mathematica says that it encounters infinite $1/0$ expressions. This seems to occur for all values of $m$ greater than $1$! Remarkably, for any other $x$, this precise error does not seem to occur anymore!?

Specifically, trying to evaluate it at a slightly different value of $x$,

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5, 1 + 1.5}, 0.901]

and Mathematica calculates for a long time (I let it run for a minute before aborting). This also occurs for larger $0.9 < x < 1$, but strangely, there is no problem for $x < 0.9$ to instantly obtain a (finite) result!?

Alternatively, trying to perturb $m$ a little bit:

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5001, 1 + 1.5001}, 0.9]

and I get a strange warning sign that Mathematica is dealing with very small numbers, below machine number.

Are there simply workarounds to compute the above values for which Mathematica has trouble with? The above mentioned messages are warning messages and Mathematica does output some (finite) value, but how safe are they?

I have trouble evaluating the following generalised hypergeometric function:

HypergeometricPFQRegularized[{1/2, 1, n/2}, {1 - m, 1 + m}, x]

at certain values of $n,m,x$.

Attempting to evaluate:

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5, 1 + 1.5}, 0.9]

and Mathematica says that it encounters infinite $1/0$ expressions. This seems to occur for all values of $m$ greater than $1$! Remarkably, for any other $x$, this precise error does not seem to occur anymore!?

Specifically, trying to evaluate it at a slightly different value of $x$,

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5, 1 + 1.5}, 0.901]

and Mathematica calculates for a long time (I let it run for a minute before aborting). This also occurs for larger $0.9 < x < 1$, but strangely, there is no problem for $x < 0.9$ to instantly obtain a (finite) result!?

Alternatively, trying to perturb $m$ a little bit:

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5001, 1 + 1.5001}, 0.9]

and I get a strange warning sign that Mathematica is dealing with very small numbers, below machine number.

Are there simply workarounds to compute the above values for which Mathematica has trouble with? The above mentioned messages are warning messages and Mathematica does output some (finite) value, but how safe are they?

I have trouble evaluating the following generalised hypergeometric function:

HypergeometricPFQRegularized[{1/2, 1, n/2}, {1 - m, 1 + m}, x]

at certain values of $n,m,x$. The Mathematica guide states that the result ought to be finite for all (finite) values of $n,m,x$.

However, attempting to evaluate:

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5, 1 + 1.5}, 0.9]

and Mathematica says that it encounters infinite $1/0$ expressions. This seems to occur for all values of $m$ greater than $1$! Remarkably, for any other $x$, this precise error does not seem to occur anymore!?

Specifically, trying to evaluate it at a slightly different value of $x$,

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5, 1 + 1.5}, 0.901]

and Mathematica calculates for a long time (I let it run for a minute before aborting). This also occurs for larger $0.9 < x < 1$, but strangely, there is no problem for $x < 0.9$ to instantly obtain a (finite) result!?

Alternatively, trying to perturb $m$ a little bit:

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5001, 1 + 1.5001}, 0.9]

and I get a strange warning sign that Mathematica is dealing with very small numbers, below machine number.

Are there simply workarounds to compute the above values for which Mathematica has trouble with?

I have trouble evaluating the following generalised hypergeometric function:

HypergeometricPFQRegularized[{1/2, 1, n/2}, {1 - m, 1 + m}, x]

at certain values of $n,m,x$. The Mathematica guide states that the result ought to be finite for all (finite) values of $n,m,x$.

However, attempting to evaluate:

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5, 1 + 1.5}, 0.9]

and Mathematica says that it encounters infinite $1/0$ expressions. This seems to occur for all values of $m$ greater than $1$! Remarkably, for any other $x$, this precise error does not seem to occur anymore!?

Specifically, trying to evaluate it at a slightly different value of $x$,

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5, 1 + 1.5}, 0.901]

and Mathematica calculates for a long time (I let it run for a minute before aborting). This also occurs for larger $0.9 < x < 1$, but strangely, there is no problem for $x < 0.9$ to instantly obtain a (finite) result!?

Alternatively, trying to perturb $m$ a little bit:

HypergeometricPFQRegularized[{1/2, 1, 1/2}, {1 - 1.5001, 1 + 1.5001}, 0.9]

and I get a strange warning sign that Mathematica is dealing with very small numbers, below machine number.

Are there simply workarounds to compute the above values for which Mathematica has trouble with? The above mentioned messages are warning messages and Mathematica does output some (finite) value, but how safe are they?