Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8466)

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`=9/2

http://functions.wolfram.com/07.22.03.8466.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 17/4}, z] == (-4 (-4321244954492928000 + 3954736715649922125 Sqrt[z] - 13164329518303263300 z + 5350223441458526400 z^(3/2) - 17590574102980032000 z^2 + 7166098459973376000 z^(5/2) - 38221389685366272000 z^3 - 4414199283037716480 z^(7/2) + 19005086803531530240 z^4 + 509029313613004800 z^(9/2) - 2093461366057205760 z^5 - 20149304945541120 z^(11/2) + 81537567824019456 z^6 + 320358120947712 z^(13/2) - 1287543953817600 z^7 - 2051920625664 z^(15/2) + 8220567404544 z^8 + 4294967296 z^(17/2) - 17179869184 z^9 + E^(4 Sqrt[z]) (4321244954492928000 + 3954736715649922125 Sqrt[z] + 13164329518303263300 z + 5350223441458526400 z^(3/2) + 17590574102980032000 z^2 + 7166098459973376000 z^(5/2) + 38221389685366272000 z^3 - 4414199283037716480 z^(7/2) - 19005086803531530240 z^4 + 509029313613004800 z^(9/2) + 2093461366057205760 z^5 - 20149304945541120 z^(11/2) - 81537567824019456 z^6 + 320358120947712 z^(13/2) + 1287543953817600 z^7 - 2051920625664 z^(15/2) - 8220567404544 z^8 + 4294967296 z^(17/2) + 17179869184 z^9)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (12597226624635778125 + 40311125198834490000 z + 57331378060564608000 z^2 + 164643957507262464000 z^3 - 77479509415182336000 z^4 + 8433143881924608000 z^5 - 327103762692833280 z^6 + 5156315471020032 z^7 - 32895154520064 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (12597226624635778125 + 40311125198834490000 z + 57331378060564608000 z^2 + 164643957507262464000 z^3 - 77479509415182336000 z^4 + 8433143881924608000 z^5 - 327103762692833280 z^6 + 5156315471020032 z^7 - 32895154520064 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (586361564171757158400 z^(7/2))

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]