Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8454)

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/07.22.03.8454.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, 5/4}, z] == (-4 (1471807260000 + 2943614520000 Sqrt[z] + 523309248000 z - 2878200864000 z^(3/2) + 1465265894400 z^2 + 7814751436800 z^(5/2) - 93777017241600 z^3 - 45403180547175 z^(7/2) + 215355669021900 z^4 + 14315413519440 z^(9/2) - 60435213030720 z^5 - 1158849308160 z^(11/2) + 4729481902080 z^6 + 32473128960 z^(13/2) - 130882633728 z^7 - 333643776 z^(15/2) + 1337720832 z^8 + 1048576 z^(17/2) - 4194304 z^9 + E^(4 Sqrt[z]) (-1471807260000 + 2943614520000 Sqrt[z] - 523309248000 z - 2878200864000 z^(3/2) - 1465265894400 z^2 + 7814751436800 z^(5/2) + 93777017241600 z^3 - 45403180547175 z^(7/2) - 215355669021900 z^4 + 14315413519440 z^(9/2) + 60435213030720 z^5 - 1158849308160 z^(11/2) - 4729481902080 z^6 + 32473128960 z^(13/2) + 130882633728 z^7 - 333643776 z^(15/2) - 1337720832 z^8 + 1048576 z^(17/2) + 4194304 z^9)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (478527127241625 - 900756945396000 z + 245103930720000 z^2 - 19014123110400 z^3 + 524527534080 z^4 - 5354029056 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (478527127241625 - 900756945396000 z + 245103930720000 z^2 - 19014123110400 z^3 + 524527534080 z^4 - 5354029056 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(2596276260864000 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]