I am encountering peculiar errors when asking MathematicaMathematica for series expansions of certain hypergeometric functions. To give an example, consider the function $f(x) = {}_{5} F_{4}(3/2,3/2,3/2,2,2; 1,5/2,5/2,5/2; e^{-x})$. I am interested in the small-x$x$ behavior, so after defining
The claimed result appears to be a bug, and involves lots of internal-looking variables like e.g. "SeriesDump`s$1186 ".SeriesDump`s$1186:
SeriesData[x, 0, {
Rational[27, 8] ((-2) EulerGamma - Log[x] - 2 PolyGamma[0,
Rational[3, 2]] + Sum[
Factorial[K$747] Factorial[1 + K$747]^(-1) Pochhammer[
Rational[-1, 2], 1 + K$747] Pochhammer[
Rational[3, 2], 1 + K$747]^(-2) Pochhammer[2, 1 + K$747] Sum[
Factorial[SeriesDump`s$1186]^(-1) HypergeometricPFQ[{
Rational[1, 2],
Rational[1, 2], -SeriesDump`s$1186}, {
1, Rational[1, 2] - SeriesDump`s$1186}, 1] Pochhammer[
Rational[1, 2], SeriesDump`s$1186] Pochhammer[1, SeriesDump`s$1186]
Pochhammer[2, SeriesDump`s$1186]^(-1) Pochhammer[-1 - K$747,
SeriesDump`s$1186]/Pochhammer[
Rational[1, 2] - K$747, SeriesDump`s$1186], {
SeriesDump`s$1186, 0, 1 + K$747}], {K$747, 0,
DirectedInfinity[1]}]),
Rational[27, 32] (21 - 20 EulerGamma - 10 Log[x] - 20 PolyGamma[0,
Rational[5,
2]] + 9 Sum[-Factorial[K$747]
Factorial[2 + K$747]^(-1) Pochhammer[
Rational[-1, 2], 2 + K$747] Pochhammer[
Rational[3, 2], 2 + K$747]^(-2) Pochhammer[2, 2 + K$747] Sum[
Factorial[SeriesDump`s$1588]^(-1) HypergeometricPFQ[{
Rational[1, 2],
Rational[1, 2], -SeriesDump`s$1588}, {
1, Rational[1, 2] - SeriesDump`s$1588}, 1] Pochhammer[
Rational[1, 2], SeriesDump`s$1588] Pochhammer[1, SeriesDump`s$1588]
Pochhammer[2, SeriesDump`s$1588]^(-1) Pochhammer[-2 - K$747,
SeriesDump`s$1588]/Pochhammer[
Rational[-1, 2] - K$747, SeriesDump`s$1588], {
SeriesDump`s$1588, 0, 2 + K$747}], {K$747, 0,
DirectedInfinity[1]}])}, 0, 2, 1]
SeriesData[x, 0, {
Rational[27, 8] ((-2) EulerGamma - Log[x] - 2 PolyGamma[0,
Rational[3, 2]] + Sum[
Factorial[K$747] Factorial[1 + K$747]^(-1) Pochhammer[
Rational[-1, 2], 1 + K$747] Pochhammer[
Rational[3, 2], 1 + K$747]^(-2) Pochhammer[2, 1 + K$747] Sum[
Factorial[SeriesDump`s$1186]^(-1) HypergeometricPFQ[{
Rational[1, 2],
Rational[1, 2], -SeriesDumps$1186}, { 1, Rational[1, 2] - SeriesDumps$1186}, 1] Pochhammer[
Rational[1, 2], SeriesDump`s$1186] Pochhammer[1, SeriesDumps$1186] Pochhammer[2, SeriesDumps$1186]^(-1) Pochhammer[-1 - K$747,
SeriesDumps$1186]/Pochhammer[ Rational[1, 2] - K$747, SeriesDumps$1186], {
SeriesDump`s$1186, 0, 1 + K$747}], {K$747, 0,
DirectedInfinity[1]}]),
Rational[27, 32] (21 - 20 EulerGamma - 10 Log[x] - 20 PolyGamma[0,
Rational[5,
2]] + 9 Sum[-Factorial[K$747]
Factorial[2 + K$747]^(-1) Pochhammer[
Rational[-1, 2], 2 + K$747] Pochhammer[
Rational[3, 2], 2 + K$747]^(-2) Pochhammer[2, 2 + K$747] Sum[
Factorial[SeriesDumps$1588]^(-1) HypergeometricPFQ[{ Rational[1, 2], Rational[1, 2], -SeriesDumps$1588}, {
1, Rational[1, 2] - SeriesDump`s$1588}, 1] Pochhammer[
Rational[1, 2], SeriesDump`s$1588] Pochhammer[1, SeriesDumps$1588] Pochhammer[2, SeriesDumps$1588]^(-1) Pochhammer[-2 - K$747,
SeriesDumps$1588]/Pochhammer[ Rational[-1, 2] - K$747, SeriesDumps$1588], {
SeriesDump`s$1588, 0, 2 + K$747}], {K$747, 0,
DirectedInfinity[1]}])}, 0, 2, 1]
All of this happens with MathematicaMathematica 10.1.0.0 running on MacOS X 10.11. To reproduce it, the minimal code is
Is this a bug in MathematicaMathematica? If it is not a bug, what am I to make of such a result?
