Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8708)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.8708.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(5/2), 19/4}, z] == (11 (4 z^(1/4) (5289558781381875 + 7052745041842500 Sqrt[z] + 2872390707950400 z - 468961748236800 z^(3/2) - 315618700400640 z^2 + 440675166597120 z^(5/2) - 186466439577600 z^3 + 461424134062080 z^(7/2) - 51519716720640 z^4 + 155655115112448 z^(9/2) - 11660169314304 z^5 + 37194584555520 z^(11/2) - 4210946998272 z^6 + 17852836872192 z^(13/2) + 351113576448 z^7 - 1417339207680 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-5289558781381875 + 7052745041842500 Sqrt[z] - 2872390707950400 z - 468961748236800 z^(3/2) + 315618700400640 z^2 + 440675166597120 z^(5/2) + 186466439577600 z^3 + 461424134062080 z^(7/2) + 51519716720640 z^4 + 155655115112448 z^(9/2) + 11660169314304 z^5 + 37194584555520 z^(11/2) + 4210946998272 z^6 + 17852836872192 z^(13/2) - 351113576448 z^7 - 1417339207680 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-5289558781381875 + 2769805325523600 z - 1205901638323200 z^2 + 882751526092800 z^3 + 1629695125094400 z^4 + 579447155589120 z^5 + 137350436880384 z^6 + 72448582090752 z^7 - 5682241732608 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-5289558781381875 + 2769805325523600 z - 1205901638323200 z^2 + 882751526092800 z^3 + 1629695125094400 z^4 + 579447155589120 z^5 + 137350436880384 z^6 + 72448582090752 z^7 - 5682241732608 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/ E^(2 Sqrt[z])/(99747694871838720 z^(15/4))

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]