Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9076)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9076.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 3/4}, z] == (-1139745481875 + 1139745481875 E^(4 Sqrt[z]) - 2279490963750 Sqrt[z] - 2279490963750 E^(4 Sqrt[z]) Sqrt[z] - 1432822891500 z + 1432822891500 E^(4 Sqrt[z]) z + 173675502000 z^(3/2) + 173675502000 E^(4 Sqrt[z]) z^(3/2) + 394717050000 z^2 - 394717050000 E^(4 Sqrt[z]) z^2 - 252618912000 z^(5/2) - 252618912000 E^(4 Sqrt[z]) z^(5/2) - 84206304000 z^3 + 84206304000 E^(4 Sqrt[z]) z^3 + 538920345600 z^(7/2) + 538920345600 E^(4 Sqrt[z]) z^(7/2) - 1616761036800 z^4 + 1616761036800 E^(4 Sqrt[z]) z^4 + 9870645657600 z^(9/2) + 9870645657600 E^(4 Sqrt[z]) z^(9/2) + 1705879866600 z^5 - 1705879866600 E^(4 Sqrt[z]) z^5 - 7461954208800 z^(11/2) - 7461954208800 E^(4 Sqrt[z]) z^(11/2) - 242493189120 z^6 + 242493189120 E^(4 Sqrt[z]) z^6 + 998215464960 z^(13/2) + 998215464960 E^(4 Sqrt[z]) z^(13/2) + 9856143360 z^7 - 9856143360 E^(4 Sqrt[z]) z^7 - 39820247040 z^(15/2) - 39820247040 E^(4 Sqrt[z]) z^(15/2) - 133693440 z^8 + 133693440 E^(4 Sqrt[z]) z^8 + 536346624 z^(17/2) + 536346624 E^(4 Sqrt[z]) z^(17/2) + 524288 z^9 - 524288 E^(4 Sqrt[z]) z^9 - 2097152 z^(19/2) - 2097152 E^(4 Sqrt[z]) z^(19/2) - 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-5487948504675 + 3817703307600 z - 502742822400 z^2 + 19960012800 z^3 - 268369920 z^4 + 1048576 z^5) Erf[Sqrt[2] z^(1/4)] + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-5487948504675 + 3817703307600 z - 502742822400 z^2 + 19960012800 z^3 - 268369920 z^4 + 1048576 z^5) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(28119150259200 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]