Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7wo)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7wo.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 23/4}, z] == (4 z^(1/4) (-60767697362770125 - 1140584109560941500 Sqrt[z] + 164548696483080000 z - 1022870647536192000 z^(3/2) + 90544411454515200 z^2 - 488749825486540800 z^(5/2) + 28699664084582400 z^3 - 228445152303513600 z^(7/2) - 51009991203225600 z^4 + 217702477277429760 z^(9/2) + 5001637118607360 z^5 - 20422680725422080 z^(11/2) - 143493515182080 z^6 + 578230104883200 z^(13/2) + 1433445335040 z^7 - 5746666242048 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (60767697362770125 - 1140584109560941500 Sqrt[z] - 164548696483080000 z - 1022870647536192000 z^(3/2) - 90544411454515200 z^2 - 488749825486540800 z^(5/2) - 28699664084582400 z^3 - 228445152303513600 z^(7/2) + 51009991203225600 z^4 + 217702477277429760 z^(9/2) - 5001637118607360 z^5 - 20422680725422080 z^(11/2) + 143493515182080 z^6 + 578230104883200 z^(13/2) - 1433445335040 z^7 - 5746666242048 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-1528573072253101875 - 4891433831209926000 z - 4065607340226432000 z^2 - 1971203558897664000 z^3 - 1051308564745420800 z^4 + 885312475575091200 z^5 - 82115939763486720 z^6 + 2317204649410560 z^7 - 22999549870080 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-1528573072253101875 - 4891433831209926000 z - 4065607340226432000 z^2 - 1971203558897664000 z^3 - 1051308564745420800 z^4 + 885312475575091200 z^5 - 82115939763486720 z^6 + 2317204649410560 z^7 - 22999549870080 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (4445006652726312960 z^(19/4))

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]