Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9526)

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`=5/2

http://functions.wolfram.com/07.22.03.9526.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, 21/4}, z] == (4 z^(1/4) (-4222757010346875 - 5630342680462500 Sqrt[z] + 2177890795080000 z + 6335682312960000 z^(3/2) - 9855505820160000 z^2 + 38061637660569600 z^(5/2) - 22431782880460800 z^3 + 129407624065843200 z^(7/2) + 19012623011020800 z^4 - 82389103843737600 z^(9/2) - 2383850231562240 z^5 + 9791973800017920 z^(11/2) + 89310489477120 z^6 - 360628271185920 z^(13/2) - 1143535042560 z^7 + 4587025072128 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-4222757010346875 + 5630342680462500 Sqrt[z] + 2177890795080000 z - 6335682312960000 z^(3/2) - 9855505820160000 z^2 - 38061637660569600 z^(5/2) - 22431782880460800 z^3 - 129407624065843200 z^(7/2) + 19012623011020800 z^4 + 82389103843737600 z^(9/2) - 2383850231562240 z^5 - 9791973800017920 z^(11/2) + 89310489477120 z^6 + 360628271185920 z^(13/2) - 1143535042560 z^7 - 4587025072128 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] (-4222757010346875 + 6682164939450000 z - 15839205782400000 z^2 - 118266069841920000 z^3 - 567677135241216000 z^4 + 336401265328128000 z^5 - 39431650148352000 z^6 + 1445927583744000 z^7 - 18360985190400 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-4222757010346875 + 6682164939450000 z - 15839205782400000 z^2 - 118266069841920000 z^3 - 567677135241216000 z^4 + 336401265328128000 z^5 - 39431650148352000 z^6 + 1445927583744000 z^7 - 18360985190400 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z])/(2181980825321472000 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]