Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9610)

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`=9/2

http://functions.wolfram.com/07.22.03.9610.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, 9/4}, z] == (4 (113762880000 + 227525760000 Sqrt[z] - 72808243200 z - 448984166400 z^(3/2) + 2378402611200 z^2 - 1873701296775 z^(5/2) + 11998661805900 z^3 + 2340424460880 z^(7/2) - 10321788882240 z^4 - 369190356480 z^(9/2) + 1523925596160 z^5 + 16530186240 z^(11/2) - 66846621696 z^6 - 245563392 z^(13/2) + 985399296 z^7 + 1048576 z^(15/2) - 4194304 z^8 + E^(4 Sqrt[z]) (-113762880000 + 227525760000 Sqrt[z] + 72808243200 z - 448984166400 z^(3/2) - 2378402611200 z^2 - 1873701296775 z^(5/2) - 11998661805900 z^3 + 2340424460880 z^(7/2) + 10321788882240 z^4 - 369190356480 z^(9/2) - 1523925596160 z^5 + 16530186240 z^(11/2) + 66846621696 z^6 - 245563392 z^(13/2) - 985399296 z^7 + 1048576 z^(15/2) + 4194304 z^8)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (7310050122375 + 53981908596000 z - 42338751840000 z^2 + 6144399360000 z^3 - 268119244800 z^4 + 3944742912 z^5 - 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(9/4) (7310050122375 + 53981908596000 z - 42338751840000 z^2 + 6144399360000 z^3 - 268119244800 z^4 + 3944742912 z^5 - 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(224542811750400 z^(7/2))

Standard Form

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MathML Form

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Rule 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]