Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7wp)

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.a7wp.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 23/4}, -z] == (Sqrt[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) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-285146027390235375 + 255717661884048000 z - 122187456371635200 z^2 + 57111288075878400 z^3 + 54425619319357440 z^4 + 5105670181355520 z^5 + 144557526220800 z^6 + 1436666560512 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (60767697362770125 + 164548696483080000 z - 90544411454515200 z^2 + 28699664084582400 z^3 + 51009991203225600 z^4 + 5001637118607360 z^5 + 143493515182080 z^6 + 1433445335040 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]]))/(1111251663181578240 z^(19/4))

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]