Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8470)

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/07.22.03.8470.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 21/4}, z] == (-4 z^(1/4) (163763946120265115625 - 703513662131471152500 Sqrt[z] + 346506621886358010000 z - 1005592057738379496000 z^(3/2) + 291851643054077568000 z^2 - 917323713971900928000 z^(5/2) + 305744742696830976000 z^3 - 1549247361856472678400 z^(7/2) - 143312864016442982400 z^4 + 610000215694442496000 z^(9/2) + 13639777247821824000 z^5 - 55880702838492364800 z^(11/2) - 461381186711715840 z^6 + 1864389580019466240 z^(13/2) + 6411382224322560 z^7 - 25754277469224960 z^(15/2) - 36485747179520 z^8 + 146149147148288 z^(17/2) + 68719476736 z^9 - 274877906944 z^(19/2) + E^(4 Sqrt[z]) (163763946120265115625 + 703513662131471152500 Sqrt[z] + 346506621886358010000 z + 1005592057738379496000 z^(3/2) + 291851643054077568000 z^2 + 917323713971900928000 z^(5/2) + 305744742696830976000 z^3 + 1549247361856472678400 z^(7/2) - 143312864016442982400 z^4 - 610000215694442496000 z^(9/2) + 13639777247821824000 z^5 + 55880702838492364800 z^(11/2) - 461381186711715840 z^6 - 1864389580019466240 z^(13/2) + 6411382224322560 z^7 + 25754277469224960 z^(15/2) - 36485747179520 z^8 - 146149147148288 z^(17/2) + 68719476736 z^9 + 274877906944 z^(19/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (163763946120265115625 + 2015556259941724500000 z + 3224890015906759200000 z^2 + 3057673496563445760000 z^3 + 6585758300290498560000 z^4 - 2479344301285834752000 z^5 + 224883836851322880000 z^6 - 7476657432979046400 z^7 + 103126309420400640 z^8 - 584802747023360 z^9 + 1099511627776 z^10) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (163763946120265115625 + 2015556259941724500000 z + 3224890015906759200000 z^2 + 3057673496563445760000 z^3 + 6585758300290498560000 z^4 - 2479344301285834752000 z^5 + 224883836851322880000 z^6 - 7476657432979046400 z^7 + 103126309420400640 z^8 - 584802747023360 z^9 + 1099511627776 z^10) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(22074788298230857728000 z^(17/4))

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]