Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9566)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9566.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 13/4}, z] == (4 (16309046476800 - 17223157880775 Sqrt[z] + 71265835802700 z - 44501921402400 z^(3/2) + 268347294230400 z^2 + 45402184154880 z^(5/2) - 198863732874240 z^3 - 6590406574080 z^(7/2) + 27163694530560 z^4 + 280639242240 z^(9/2) - 1134469840896 z^5 - 4028628992 z^(11/2) + 16164847616 z^6 + 16777216 z^(13/2) - 67108864 z^7 + E^(4 Sqrt[z]) (-16309046476800 - 17223157880775 Sqrt[z] - 71265835802700 z - 44501921402400 z^(3/2) - 268347294230400 z^2 + 45402184154880 z^(5/2) + 198863732874240 z^3 - 6590406574080 z^(7/2) - 27163694530560 z^4 + 280639242240 z^(9/2) + 1134469840896 z^5 - 4028628992 z^(11/2) - 16164847616 z^6 + 16777216 z^(13/2) + 67108864 z^7)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (49841250834375 + 223288803738000 z + 1190873619936000 z^2 - 814272560640000 z^3 + 109482024960000 z^4 - 4549902336000 z^5 + 64709722112 z^6 - 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (49841250834375 + 223288803738000 z + 1190873619936000 z^2 - 814272560640000 z^3 + 109482024960000 z^4 - 4549902336000 z^5 + 64709722112 z^6 - 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(4741860320870400 z^(5/2))

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]