Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8506)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8506.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 9/4}, z] == (-4 (576948445920000 + 1153896891840000 Sqrt[z] + 402948120960000 z - 732632947200000 z^(3/2) - 5861063577600 z^2 + 1375396252876800 z^(5/2) - 6376837172428800 z^3 + 4615289458250625 z^(7/2) - 28856367159196500 z^4 - 5422837959776160 z^(9/2) + 23985975146474880 z^5 + 896976055422720 z^(11/2) - 3717870145920000 z^6 - 46213222809600 z^(13/2) + 187501168361472 z^7 + 905932898304 z^(15/2) - 3644276342784 z^8 - 6905921536 z^(17/2) + 27674017792 z^9 + 16777216 z^(19/2) - 67108864 z^10 + E^(4 Sqrt[z]) (-576948445920000 + 1153896891840000 Sqrt[z] - 402948120960000 z - 732632947200000 z^(3/2) + 5861063577600 z^2 + 1375396252876800 z^(5/2) + 6376837172428800 z^3 + 4615289458250625 z^(7/2) + 28856367159196500 z^4 - 5422837959776160 z^(9/2) - 23985975146474880 z^5 + 896976055422720 z^(11/2) + 3717870145920000 z^6 - 46213222809600 z^(13/2) - 187501168361472 z^7 + 905932898304 z^(15/2) + 3644276342784 z^8 - 6905921536 z^(17/2) - 27674017792 z^9 + 16777216 z^(19/2) + 67108864 z^10)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (19619612216906625 + 129258621664326000 z - 98482759363296000 z^2 + 15006896664883200 z^3 - 752697011404800 z^4 + 14597760221184 z^5 - 110746402816 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (19619612216906625 + 129258621664326000 z - 98482759363296000 z^2 + 15006896664883200 z^3 - 752697011404800 z^4 + 14597760221184 z^5 - 110746402816 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (529871137328332800 z^(9/2))

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]