Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a91y)

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

For fixed z and a₁=-11/4, b_1`=1/2

http://functions.wolfram.com/07.22.03.a91y.01

Input Form

HypergeometricPFQ[{-(11/4)}, {1/2, 21/4}, z] == -((221 (-4 z^(1/4) (-21070924875 - 28094566500 Sqrt[z] - 10373378400 z + 3293136000 z^(3/2) + 1333221120 z^2 - 2522741760 z^(5/2) + 851558400 z^3 + 3406233600 z^(7/2) + 4149411840 z^4 - 18557435904 z^(9/2) - 710934528 z^5 + 2894069760 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (-21070924875 + 28094566500 Sqrt[z] - 10373378400 z - 3293136000 z^(3/2) + 1333221120 z^2 + 2522741760 z^(5/2) + 851558400 z^3 - 3406233600 z^(7/2) + 4149411840 z^4 + 18557435904 z^(9/2) - 710934528 z^5 - 2894069760 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-21070924875 + 12102274800 z - 5867769600 z^2 + 4470681600 z^3 - 23843635200 z^4 + 76299632640 z^5 - 11626610688 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-21070924875 + 12102274800 z - 5867769600 z^2 + 4470681600 z^3 - 23843635200 z^4 + 76299632640 z^5 - 11626610688 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(43293270343680 z^(17/4)))

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]